KILLED
proof of input_YyzBmuqbS2.trs
# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished


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

(0) CpxTRS
(1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxTRS
(3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(4) CpxTRS
(5) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(6) CdtProblem
    (7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CpxRelTRS
    (9) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) CpxRelTRS
    (11) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (12) typed CpxTrs
    (13) OrderProof [LOWER BOUND(ID), 0 ms]
    (14) typed CpxTrs
    (15) RewriteLemmaProof [LOWER BOUND(ID), 2251 ms]
    (16) typed CpxTrs
    (17) RewriteLemmaProof [LOWER BOUND(ID), 477 ms]
    (18) typed CpxTrs
    (19) RewriteLemmaProof [LOWER BOUND(ID), 453 ms]
    (20) typed CpxTrs
    (21) RewriteLemmaProof [LOWER BOUND(ID), 448 ms]
    (22) typed CpxTrs
    (23) RewriteLemmaProof [LOWER BOUND(ID), 145 ms]
    (24) typed CpxTrs
    (25) RewriteLemmaProof [LOWER BOUND(ID), 193 ms]
    (26) typed CpxTrs
    (27) RewriteLemmaProof [LOWER BOUND(ID), 191 ms]
    (28) typed CpxTrs
    (29) RewriteLemmaProof [LOWER BOUND(ID), 113 ms]
    (30) typed CpxTrs
    (31) RewriteLemmaProof [LOWER BOUND(ID), 437 ms]
    (32) typed CpxTrs
    (33) RewriteLemmaProof [LOWER BOUND(ID), 398 ms]
    (34) typed CpxTrs
    (35) RewriteLemmaProof [LOWER BOUND(ID), 408 ms]
    (36) typed CpxTrs
    (37) RewriteLemmaProof [LOWER BOUND(ID), 211 ms]
    (38) typed CpxTrs
    (39) RewriteLemmaProof [LOWER BOUND(ID), 194 ms]
    (40) typed CpxTrs
    (41) RewriteLemmaProof [LOWER BOUND(ID), 437 ms]
    (42) BEST
        (43) proven lower bound
            (44) LowerBoundPropagationProof [FINISHED, 0 ms]
            (45) BOUNDS(n^1, INF)
        (46) typed CpxTrs
            (47) RewriteLemmaProof [LOWER BOUND(ID), 447 ms]
            (48) typed CpxTrs
            (49) RewriteLemmaProof [LOWER BOUND(ID), 2581 ms]
            (50) typed CpxTrs
            (51) RewriteLemmaProof [LOWER BOUND(ID), 459 ms]
            (52) typed CpxTrs
            (53) RewriteLemmaProof [LOWER BOUND(ID), 626 ms]
            (54) typed CpxTrs
            (55) RewriteLemmaProof [LOWER BOUND(ID), 441 ms]
            (56) typed CpxTrs
            (57) RewriteLemmaProof [LOWER BOUND(ID), 2507 ms]
            (58) BOUNDS(1, INF)
(59) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(60) CdtProblem
    (61) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (62) CdtProblem
    (63) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (64) CpxRelTRS
        (65) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
        (66) CpxTRS
        (67) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (68) CpxWeightedTrs
            (69) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
            (70) CpxTypedWeightedTrs
            (71) CompletionProof [UPPER BOUND(ID), 0 ms]
            (72) CpxTypedWeightedCompleteTrs
                (73) NarrowingProof [BOTH BOUNDS(ID, ID), 51.9 s]
                (74) CpxTypedWeightedCompleteTrs
                (75) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
                (76) CpxRNTS
                (77) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
                (78) CpxRNTS
            (79) CompletionProof [UPPER BOUND(ID), 0 ms]
            (80) CpxTypedWeightedCompleteTrs
                (81) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
                (82) CpxRNTS
    (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 11 ms]
    (84) CdtProblem
        (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (86) CdtProblem
        (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (88) CdtProblem
        (89) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (90) CdtProblem
        (91) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (92) CdtProblem
        (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3 ms]
        (94) CdtProblem
        (95) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (96) CdtProblem
        (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (98) CdtProblem
        (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (100) CdtProblem
        (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (102) CdtProblem
        (103) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (104) CdtProblem
        (105) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (106) CdtProblem
        (107) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3 ms]
        (108) CdtProblem
        (109) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (110) CdtProblem
        (111) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (112) CdtProblem
        (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 26 ms]
        (114) CdtProblem
        (115) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (116) CdtProblem
        (117) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (118) CdtProblem
        (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1 ms]
        (120) CdtProblem
        (121) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (122) CdtProblem
        (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 45 ms]
        (124) CdtProblem
        (125) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (126) CdtProblem
        (127) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (128) CdtProblem
        (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 25 ms]
        (130) CdtProblem
        (131) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (132) CdtProblem
        (133) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (134) CdtProblem
        (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms]
        (136) CdtProblem
        (137) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (138) CdtProblem
        (139) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 10 ms]
        (140) CdtProblem
        (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 36 ms]
        (142) CdtProblem
        (143) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (144) CdtProblem
        (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 17 ms]
        (146) CdtProblem
        (147) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 1 ms]
        (148) CdtProblem
        (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 25 ms]
        (150) CdtProblem
        (151) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (152) CdtProblem
        (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 40 ms]
        (154) CdtProblem
        (155) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 12 ms]
        (156) CdtProblem
        (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 56 ms]
        (158) CdtProblem
        (159) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (160) CdtProblem
        (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 50 ms]
        (162) CdtProblem
        (163) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (164) CdtProblem
        (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1 ms]
        (166) CdtProblem
        (167) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (168) CdtProblem
        (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 79 ms]
        (170) CdtProblem
        (171) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (172) CdtProblem
        (173) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 19 ms]
        (174) CdtProblem
        (175) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (176) CdtProblem
        (177) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 38 ms]
        (178) CdtProblem
        (179) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (180) CdtProblem
        (181) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 40 ms]
        (182) CdtProblem
        (183) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (184) CdtProblem
        (185) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 40 ms]
        (186) CdtProblem
        (187) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (188) CdtProblem
        (189) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 35 ms]
        (190) CdtProblem
        (191) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (192) CdtProblem
        (193) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 47 ms]
        (194) CdtProblem
        (195) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (196) CdtProblem
        (197) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 26 ms]
        (198) CdtProblem
        (199) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (200) CdtProblem
        (201) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 31 ms]
        (202) CdtProblem
        (203) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (204) CdtProblem
        (205) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (206) CdtProblem
        (207) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 8 ms]
        (208) CdtProblem
        (209) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 41 ms]
        (210) CdtProblem
        (211) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (212) CdtProblem
        (213) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 41 ms]
        (214) CdtProblem
        (215) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (216) CdtProblem
        (217) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 26 ms]
        (218) CdtProblem
        (219) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (220) CdtProblem
        (221) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 25 ms]
        (222) CdtProblem
        (223) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 7 ms]
        (224) CdtProblem
        (225) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (226) CdtProblem
        (227) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (228) CdtProblem
        (229) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (230) CdtProblem
        (231) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (232) CdtProblem
        (233) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 71 ms]
        (234) CdtProblem
        (235) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (236) CdtProblem
        (237) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms]
        (238) CdtProblem
        (239) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 59 ms]
        (240) CdtProblem
        (241) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (242) CdtProblem
        (243) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (244) CdtProblem
        (245) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 58 ms]
        (246) CdtProblem
        (247) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (248) CdtProblem
        (249) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (250) CdtProblem
        (251) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 30 ms]
        (252) CdtProblem
        (253) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 12 ms]
        (254) CdtProblem
        (255) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 14 ms]
        (256) CdtProblem
        (257) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 81 ms]
        (258) CdtProblem
        (259) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (260) CdtProblem
        (261) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (262) CdtProblem
        (263) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 52 ms]
        (264) CdtProblem
        (265) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 4 ms]
        (266) CdtProblem
        (267) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (268) CdtProblem
(269) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms]
(270) CpxWeightedTrs
    (271) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (272) CpxTypedWeightedTrs
    (273) CompletionProof [UPPER BOUND(ID), 0 ms]
    (274) CpxTypedWeightedCompleteTrs
        (275) NarrowingProof [BOTH BOUNDS(ID, ID), 307 ms]
        (276) CpxTypedWeightedCompleteTrs
        (277) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (278) CpxRNTS
        (279) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (280) CpxRNTS
    (281) CompletionProof [UPPER BOUND(ID), 0 ms]
    (282) CpxTypedWeightedCompleteTrs
        (283) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (284) CpxRNTS


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

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


The TRS R consists of the following rules:

   a__U11(tt, M, N) -> a__U12(tt, M, N)
   a__U12(tt, M, N) -> s(a__plus(mark(N), mark(M)))
   a__U21(tt, M, N) -> a__U22(tt, M, N)
   a__U22(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
   a__plus(N, 0) -> mark(N)
   a__plus(N, s(M)) -> a__U11(tt, M, N)
   a__x(N, 0) -> 0
   a__x(N, s(M)) -> a__U21(tt, M, N)
   mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
   mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
   mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
   mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3)
   mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
   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, X3) -> U12(X1, X2, X3)
   a__plus(X1, X2) -> plus(X1, X2)
   a__U21(X1, X2, X3) -> U21(X1, X2, X3)
   a__U22(X1, X2, X3) -> U22(X1, X2, X3)
   a__x(X1, X2) -> x(X1, X2)

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, M, N) -> a__U12(tt, M, N)
   a__U12(tt, M, N) -> s(a__plus(mark(N), mark(M)))
   a__U21(tt, M, N) -> a__U22(tt, M, N)
   a__U22(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
   a__plus(N, 0') -> mark(N)
   a__plus(N, s(M)) -> a__U11(tt, M, N)
   a__x(N, 0') -> 0'
   a__x(N, s(M)) -> a__U21(tt, M, N)
   mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
   mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
   mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
   mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3)
   mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
   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, X3) -> U12(X1, X2, X3)
   a__plus(X1, X2) -> plus(X1, X2)
   a__U21(X1, X2, X3) -> U21(X1, X2, X3)
   a__U22(X1, X2, X3) -> U22(X1, X2, X3)
   a__x(X1, X2) -> x(X1, X2)

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, M, N) -> a__U12(tt, M, N)
   a__U12(tt, M, N) -> s(a__plus(mark(N), mark(M)))
   a__U21(tt, M, N) -> a__U22(tt, M, N)
   a__U22(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N))
   a__plus(N, 0) -> mark(N)
   a__plus(N, s(M)) -> a__U11(tt, M, N)
   a__x(N, 0) -> 0
   a__x(N, s(M)) -> a__U21(tt, M, N)
   mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3)
   mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3)
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
   mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3)
   mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3)
   mark(x(X1, X2)) -> a__x(mark(X1), mark(X2))
   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, X3) -> U12(X1, X2, X3)
   a__plus(X1, X2) -> plus(X1, X2)
   a__U21(X1, X2, X3) -> U21(X1, X2, X3)
   a__U22(X1, X2, X3) -> U22(X1, X2, X3)
   a__x(X1, X2) -> x(X1, X2)

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

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

(6)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U11(z0, z1, z2) -> c1
   A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U12(z0, z1, z2) -> c4
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__U21(z0, z1, z2) -> c6
   A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__U22(z0, z1, z2) -> c10
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__PLUS(z0, z1) -> c13
   A__X(z0, 0) -> c14
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   A__X(z0, z1) -> c16
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(tt) -> c25
   MARK(s(z0)) -> c26(MARK(z0))
   MARK(0) -> c27
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U11(z0, z1, z2) -> c1
   A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U12(z0, z1, z2) -> c4
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__U21(z0, z1, z2) -> c6
   A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__U22(z0, z1, z2) -> c10
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__PLUS(z0, z1) -> c13
   A__X(z0, 0) -> c14
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   A__X(z0, z1) -> c16
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(tt) -> c25
   MARK(s(z0)) -> c26(MARK(z0))
   MARK(0) -> c27
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U12_3, A__U21_3, A__U22_3, A__PLUS_2, A__X_2, MARK_1

Compound Symbols:   c_1, c1, c2_2, c3_2, c4, c5_1, c6, c7_3, c8_3, c9_2, c10, c11_1, c12_1, c13, c14, c15_1, c16, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c25, c26_1, c27


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

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

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


The TRS R consists of the following rules:

   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U11(z0, z1, z2) -> c1
   A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U12(z0, z1, z2) -> c4
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__U21(z0, z1, z2) -> c6
   A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__U22(z0, z1, z2) -> c10
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__PLUS(z0, z1) -> c13
   A__X(z0, 0) -> c14
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   A__X(z0, z1) -> c16
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(tt) -> c25
   MARK(s(z0)) -> c26(MARK(z0))
   MARK(0) -> c27

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

   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0

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

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

(10)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF).


The TRS R consists of the following rules:

   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U11(z0, z1, z2) -> c1
   A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U12(z0, z1, z2) -> c4
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__U21(z0, z1, z2) -> c6
   A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__U22(z0, z1, z2) -> c10
   A__PLUS(z0, 0') -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__PLUS(z0, z1) -> c13
   A__X(z0, 0') -> c14
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   A__X(z0, z1) -> c16
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(tt) -> c25
   MARK(s(z0)) -> c26(MARK(z0))
   MARK(0') -> c27

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

   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0') -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0') -> 0'
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0') -> 0'

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

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

(12)
Obligation:
Innermost TRS:
Rules:
A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
A__U11(z0, z1, z2) -> c1
A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U12(z0, z1, z2) -> c4
A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
A__U21(z0, z1, z2) -> c6
A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U22(z0, z1, z2) -> c10
A__PLUS(z0, 0') -> c11(MARK(z0))
A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
A__PLUS(z0, z1) -> c13
A__X(z0, 0') -> c14
A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
A__X(z0, z1) -> c16
MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(tt) -> c25
MARK(s(z0)) -> c26(MARK(z0))
MARK(0') -> c27
a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
a__U11(z0, z1, z2) -> U11(z0, z1, z2)
a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U12(z0, z1, z2) -> U12(z0, z1, z2)
a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U22(z0, z1, z2) -> U22(z0, z1, z2)
a__plus(z0, 0') -> mark(z0)
a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> 0'
a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c:c1
tt :: tt:0':s:U11:U12:plus:U21:U22:x
c :: c2:c3:c4 -> c:c1
A__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c2:c3:c4
c1 :: c:c1
c2 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
A__PLUS :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c11:c12:c13
mark :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
MARK :: tt:0':s:U11:U12:plus:U21:U22:x -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c3 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
c4 :: c2:c3:c4
A__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c5:c6
c5 :: c7:c8:c9:c10 -> c5:c6
A__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c7:c8:c9:c10
c6 :: c5:c6
c7 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
a__x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
A__X :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c14:c15:c16
c8 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c9 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
0' :: tt:0':s:U11:U12:plus:U21:U22:x
c11 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c11:c12:c13
s :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c12 :: c:c1 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c14:c15:c16
c15 :: c5:c6 -> c14:c15:c16
c16 :: c14:c15:c16
U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c17 :: c:c1 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c18 :: c2:c3:c4 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c19 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c20 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c21 :: c5:c6 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c22 :: c7:c8:c9:c10 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c23 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c24 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c25 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c26 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c27 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
a__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
hole_c:c11_28 :: c:c1
hole_tt:0':s:U11:U12:plus:U21:U22:x2_28 :: tt:0':s:U11:U12:plus:U21:U22:x
hole_c2:c3:c43_28 :: c2:c3:c4
hole_c11:c12:c134_28 :: c11:c12:c13
hole_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c275_28 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
hole_c5:c66_28 :: c5:c6
hole_c7:c8:c9:c107_28 :: c7:c8:c9:c10
hole_c14:c15:c168_28 :: c14:c15:c16
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28 :: Nat -> tt:0':s:U11:U12:plus:U21:U22:x
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28 :: Nat -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27

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

(13) OrderProof (LOWER BOUND(ID))
Heuristically decided to analyse the following defined symbols:
A__U11, A__U12, A__PLUS, mark, MARK, A__U21, A__U22, a__x, A__X, a__U11, a__U12, a__plus, a__U21, a__U22

They will be analysed ascendingly in the following order:
A__U11 = A__U12
A__U11 = A__PLUS
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__U22
A__U11 = A__X
A__U12 = A__PLUS
mark < A__U12
A__U12 = MARK
A__U12 = A__U21
A__U12 = A__U22
A__U12 = A__X
A__PLUS = MARK
A__PLUS = A__U21
A__PLUS = A__U22
A__PLUS = A__X
mark < MARK
mark < A__U22
mark = a__x
mark = a__U11
mark = a__U12
mark = a__plus
mark = a__U21
mark = a__U22
MARK = A__U21
MARK = A__U22
MARK = A__X
A__U21 = A__U22
A__U21 = A__X
a__x < A__U22
A__U22 = A__X
a__x = a__U11
a__x = a__U12
a__x = a__plus
a__x = a__U21
a__x = a__U22
a__U11 = a__U12
a__U11 = a__plus
a__U11 = a__U21
a__U11 = a__U22
a__U12 = a__plus
a__U12 = a__U21
a__U12 = a__U22
a__plus = a__U21
a__plus = a__U22
a__U21 = a__U22

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

(14)
Obligation:
Innermost TRS:
Rules:
A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
A__U11(z0, z1, z2) -> c1
A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U12(z0, z1, z2) -> c4
A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
A__U21(z0, z1, z2) -> c6
A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U22(z0, z1, z2) -> c10
A__PLUS(z0, 0') -> c11(MARK(z0))
A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
A__PLUS(z0, z1) -> c13
A__X(z0, 0') -> c14
A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
A__X(z0, z1) -> c16
MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(tt) -> c25
MARK(s(z0)) -> c26(MARK(z0))
MARK(0') -> c27
a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
a__U11(z0, z1, z2) -> U11(z0, z1, z2)
a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U12(z0, z1, z2) -> U12(z0, z1, z2)
a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U22(z0, z1, z2) -> U22(z0, z1, z2)
a__plus(z0, 0') -> mark(z0)
a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> 0'
a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c:c1
tt :: tt:0':s:U11:U12:plus:U21:U22:x
c :: c2:c3:c4 -> c:c1
A__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c2:c3:c4
c1 :: c:c1
c2 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
A__PLUS :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c11:c12:c13
mark :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
MARK :: tt:0':s:U11:U12:plus:U21:U22:x -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c3 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
c4 :: c2:c3:c4
A__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c5:c6
c5 :: c7:c8:c9:c10 -> c5:c6
A__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c7:c8:c9:c10
c6 :: c5:c6
c7 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
a__x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
A__X :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c14:c15:c16
c8 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c9 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
0' :: tt:0':s:U11:U12:plus:U21:U22:x
c11 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c11:c12:c13
s :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c12 :: c:c1 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c14:c15:c16
c15 :: c5:c6 -> c14:c15:c16
c16 :: c14:c15:c16
U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c17 :: c:c1 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c18 :: c2:c3:c4 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c19 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c20 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c21 :: c5:c6 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c22 :: c7:c8:c9:c10 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c23 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c24 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c25 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c26 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c27 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
a__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
hole_c:c11_28 :: c:c1
hole_tt:0':s:U11:U12:plus:U21:U22:x2_28 :: tt:0':s:U11:U12:plus:U21:U22:x
hole_c2:c3:c43_28 :: c2:c3:c4
hole_c11:c12:c134_28 :: c11:c12:c13
hole_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c275_28 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
hole_c5:c66_28 :: c5:c6
hole_c7:c8:c9:c107_28 :: c7:c8:c9:c10
hole_c14:c15:c168_28 :: c14:c15:c16
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28 :: Nat -> tt:0':s:U11:U12:plus:U21:U22:x
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28 :: Nat -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27


Generator Equations:
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0) <=> tt
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(x))
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(0) <=> c25
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(+(x, 1)) <=> c17(c(c2(c11(c25), c25)), gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(x))


The following defined symbols remain to be analysed:
a__U11, A__U11, A__U12, A__PLUS, mark, MARK, A__U21, A__U22, a__x, A__X, a__U12, a__plus, a__U21, a__U22

They will be analysed ascendingly in the following order:
A__U11 = A__U12
A__U11 = A__PLUS
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__U22
A__U11 = A__X
A__U12 = A__PLUS
mark < A__U12
A__U12 = MARK
A__U12 = A__U21
A__U12 = A__U22
A__U12 = A__X
A__PLUS = MARK
A__PLUS = A__U21
A__PLUS = A__U22
A__PLUS = A__X
mark < MARK
mark < A__U22
mark = a__x
mark = a__U11
mark = a__U12
mark = a__plus
mark = a__U21
mark = a__U22
MARK = A__U21
MARK = A__U22
MARK = A__X
A__U21 = A__U22
A__U21 = A__X
a__x < A__U22
A__U22 = A__X
a__x = a__U11
a__x = a__U12
a__x = a__plus
a__x = a__U21
a__x = a__U22
a__U11 = a__U12
a__U11 = a__plus
a__U11 = a__U21
a__U11 = a__U22
a__U12 = a__plus
a__U12 = a__U21
a__U12 = a__U22
a__plus = a__U21
a__plus = a__U22
a__U21 = a__U22

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

(15) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n128626_28)) -> gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n128626_28), rt in Omega(0)

Induction Base:
mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0)) ->_R^Omega(0)
tt

Induction Step:
mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(n128626_28, 1))) ->_R^Omega(0)
s(mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n128626_28))) ->_IH
s(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c128627_28))

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(16)
Obligation:
Innermost TRS:
Rules:
A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
A__U11(z0, z1, z2) -> c1
A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U12(z0, z1, z2) -> c4
A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
A__U21(z0, z1, z2) -> c6
A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U22(z0, z1, z2) -> c10
A__PLUS(z0, 0') -> c11(MARK(z0))
A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
A__PLUS(z0, z1) -> c13
A__X(z0, 0') -> c14
A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
A__X(z0, z1) -> c16
MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(tt) -> c25
MARK(s(z0)) -> c26(MARK(z0))
MARK(0') -> c27
a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
a__U11(z0, z1, z2) -> U11(z0, z1, z2)
a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U12(z0, z1, z2) -> U12(z0, z1, z2)
a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U22(z0, z1, z2) -> U22(z0, z1, z2)
a__plus(z0, 0') -> mark(z0)
a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> 0'
a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c:c1
tt :: tt:0':s:U11:U12:plus:U21:U22:x
c :: c2:c3:c4 -> c:c1
A__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c2:c3:c4
c1 :: c:c1
c2 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
A__PLUS :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c11:c12:c13
mark :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
MARK :: tt:0':s:U11:U12:plus:U21:U22:x -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c3 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
c4 :: c2:c3:c4
A__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c5:c6
c5 :: c7:c8:c9:c10 -> c5:c6
A__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c7:c8:c9:c10
c6 :: c5:c6
c7 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
a__x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
A__X :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c14:c15:c16
c8 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c9 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
0' :: tt:0':s:U11:U12:plus:U21:U22:x
c11 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c11:c12:c13
s :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c12 :: c:c1 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c14:c15:c16
c15 :: c5:c6 -> c14:c15:c16
c16 :: c14:c15:c16
U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c17 :: c:c1 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c18 :: c2:c3:c4 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c19 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c20 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c21 :: c5:c6 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c22 :: c7:c8:c9:c10 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c23 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c24 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c25 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c26 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c27 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
a__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
hole_c:c11_28 :: c:c1
hole_tt:0':s:U11:U12:plus:U21:U22:x2_28 :: tt:0':s:U11:U12:plus:U21:U22:x
hole_c2:c3:c43_28 :: c2:c3:c4
hole_c11:c12:c134_28 :: c11:c12:c13
hole_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c275_28 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
hole_c5:c66_28 :: c5:c6
hole_c7:c8:c9:c107_28 :: c7:c8:c9:c10
hole_c14:c15:c168_28 :: c14:c15:c16
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28 :: Nat -> tt:0':s:U11:U12:plus:U21:U22:x
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28 :: Nat -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27


Lemmas:
mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n128626_28)) -> gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n128626_28), rt in Omega(0)


Generator Equations:
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0) <=> tt
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(x))
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(0) <=> c25
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(+(x, 1)) <=> c17(c(c2(c11(c25), c25)), gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(x))


The following defined symbols remain to be analysed:
a__U21, A__U11, A__U12, A__PLUS, MARK, A__U21, A__U22, a__x, A__X, a__U11, a__U12, a__plus, a__U22

They will be analysed ascendingly in the following order:
A__U11 = A__U12
A__U11 = A__PLUS
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__U22
A__U11 = A__X
A__U12 = A__PLUS
mark < A__U12
A__U12 = MARK
A__U12 = A__U21
A__U12 = A__U22
A__U12 = A__X
A__PLUS = MARK
A__PLUS = A__U21
A__PLUS = A__U22
A__PLUS = A__X
mark < MARK
mark < A__U22
mark = a__x
mark = a__U11
mark = a__U12
mark = a__plus
mark = a__U21
mark = a__U22
MARK = A__U21
MARK = A__U22
MARK = A__X
A__U21 = A__U22
A__U21 = A__X
a__x < A__U22
A__U22 = A__X
a__x = a__U11
a__x = a__U12
a__x = a__plus
a__x = a__U21
a__x = a__U22
a__U11 = a__U12
a__U11 = a__plus
a__U11 = a__U21
a__U11 = a__U22
a__U12 = a__plus
a__U12 = a__U21
a__U12 = a__U22
a__plus = a__U21
a__plus = a__U22
a__U21 = a__U22

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

(17) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
a__U21(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n136054_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)

Induction Base:
a__U21(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))

Induction Step:
a__U21(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(n136054_28, 1)), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) ->_R^Omega(0)
a__U22(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(n136054_28, 1)), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) ->_R^Omega(0)
a__plus(a__x(mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n136054_28)))), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_L^Omega(0)
a__plus(a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n136054_28)))), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_L^Omega(0)
a__plus(a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n136054_28))), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_R^Omega(0)
a__plus(a__U21(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n136054_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_IH
a__plus(*11_28, mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_L^Omega(0)
a__plus(*11_28, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(18)
Obligation:
Innermost TRS:
Rules:
A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
A__U11(z0, z1, z2) -> c1
A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U12(z0, z1, z2) -> c4
A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
A__U21(z0, z1, z2) -> c6
A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U22(z0, z1, z2) -> c10
A__PLUS(z0, 0') -> c11(MARK(z0))
A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
A__PLUS(z0, z1) -> c13
A__X(z0, 0') -> c14
A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
A__X(z0, z1) -> c16
MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(tt) -> c25
MARK(s(z0)) -> c26(MARK(z0))
MARK(0') -> c27
a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
a__U11(z0, z1, z2) -> U11(z0, z1, z2)
a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U12(z0, z1, z2) -> U12(z0, z1, z2)
a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U22(z0, z1, z2) -> U22(z0, z1, z2)
a__plus(z0, 0') -> mark(z0)
a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> 0'
a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c:c1
tt :: tt:0':s:U11:U12:plus:U21:U22:x
c :: c2:c3:c4 -> c:c1
A__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c2:c3:c4
c1 :: c:c1
c2 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
A__PLUS :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c11:c12:c13
mark :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
MARK :: tt:0':s:U11:U12:plus:U21:U22:x -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c3 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
c4 :: c2:c3:c4
A__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c5:c6
c5 :: c7:c8:c9:c10 -> c5:c6
A__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c7:c8:c9:c10
c6 :: c5:c6
c7 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
a__x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
A__X :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c14:c15:c16
c8 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c9 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
0' :: tt:0':s:U11:U12:plus:U21:U22:x
c11 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c11:c12:c13
s :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c12 :: c:c1 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c14:c15:c16
c15 :: c5:c6 -> c14:c15:c16
c16 :: c14:c15:c16
U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c17 :: c:c1 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c18 :: c2:c3:c4 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c19 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c20 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c21 :: c5:c6 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c22 :: c7:c8:c9:c10 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c23 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c24 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c25 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c26 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c27 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
a__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
hole_c:c11_28 :: c:c1
hole_tt:0':s:U11:U12:plus:U21:U22:x2_28 :: tt:0':s:U11:U12:plus:U21:U22:x
hole_c2:c3:c43_28 :: c2:c3:c4
hole_c11:c12:c134_28 :: c11:c12:c13
hole_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c275_28 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
hole_c5:c66_28 :: c5:c6
hole_c7:c8:c9:c107_28 :: c7:c8:c9:c10
hole_c14:c15:c168_28 :: c14:c15:c16
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28 :: Nat -> tt:0':s:U11:U12:plus:U21:U22:x
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28 :: Nat -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27


Lemmas:
mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n128626_28)) -> gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n128626_28), rt in Omega(0)
a__U21(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n136054_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)


Generator Equations:
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0) <=> tt
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(x))
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(0) <=> c25
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(+(x, 1)) <=> c17(c(c2(c11(c25), c25)), gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(x))


The following defined symbols remain to be analysed:
a__U22, A__U11, A__U12, A__PLUS, mark, MARK, A__U21, A__U22, a__x, A__X, a__U11, a__U12, a__plus

They will be analysed ascendingly in the following order:
A__U11 = A__U12
A__U11 = A__PLUS
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__U22
A__U11 = A__X
A__U12 = A__PLUS
mark < A__U12
A__U12 = MARK
A__U12 = A__U21
A__U12 = A__U22
A__U12 = A__X
A__PLUS = MARK
A__PLUS = A__U21
A__PLUS = A__U22
A__PLUS = A__X
mark < MARK
mark < A__U22
mark = a__x
mark = a__U11
mark = a__U12
mark = a__plus
mark = a__U21
mark = a__U22
MARK = A__U21
MARK = A__U22
MARK = A__X
A__U21 = A__U22
A__U21 = A__X
a__x < A__U22
A__U22 = A__X
a__x = a__U11
a__x = a__U12
a__x = a__plus
a__x = a__U21
a__x = a__U22
a__U11 = a__U12
a__U11 = a__plus
a__U11 = a__U21
a__U11 = a__U22
a__U12 = a__plus
a__U12 = a__U21
a__U12 = a__U22
a__plus = a__U21
a__plus = a__U22
a__U21 = a__U22

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

(19) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
a__U22(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n155326_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)

Induction Base:
a__U22(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))

Induction Step:
a__U22(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(n155326_28, 1)), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) ->_R^Omega(0)
a__plus(a__x(mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(n155326_28, 1)))), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_L^Omega(0)
a__plus(a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n155326_28)))), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_L^Omega(0)
a__plus(a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n155326_28))), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_R^Omega(0)
a__plus(a__U21(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n155326_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_R^Omega(0)
a__plus(a__U22(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n155326_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_IH
a__plus(*11_28, mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_L^Omega(0)
a__plus(*11_28, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(20)
Obligation:
Innermost TRS:
Rules:
A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
A__U11(z0, z1, z2) -> c1
A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U12(z0, z1, z2) -> c4
A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
A__U21(z0, z1, z2) -> c6
A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U22(z0, z1, z2) -> c10
A__PLUS(z0, 0') -> c11(MARK(z0))
A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
A__PLUS(z0, z1) -> c13
A__X(z0, 0') -> c14
A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
A__X(z0, z1) -> c16
MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(tt) -> c25
MARK(s(z0)) -> c26(MARK(z0))
MARK(0') -> c27
a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
a__U11(z0, z1, z2) -> U11(z0, z1, z2)
a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U12(z0, z1, z2) -> U12(z0, z1, z2)
a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U22(z0, z1, z2) -> U22(z0, z1, z2)
a__plus(z0, 0') -> mark(z0)
a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> 0'
a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c:c1
tt :: tt:0':s:U11:U12:plus:U21:U22:x
c :: c2:c3:c4 -> c:c1
A__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c2:c3:c4
c1 :: c:c1
c2 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
A__PLUS :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c11:c12:c13
mark :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
MARK :: tt:0':s:U11:U12:plus:U21:U22:x -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c3 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
c4 :: c2:c3:c4
A__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c5:c6
c5 :: c7:c8:c9:c10 -> c5:c6
A__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c7:c8:c9:c10
c6 :: c5:c6
c7 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
a__x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
A__X :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c14:c15:c16
c8 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c9 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
0' :: tt:0':s:U11:U12:plus:U21:U22:x
c11 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c11:c12:c13
s :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c12 :: c:c1 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c14:c15:c16
c15 :: c5:c6 -> c14:c15:c16
c16 :: c14:c15:c16
U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c17 :: c:c1 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c18 :: c2:c3:c4 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c19 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c20 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c21 :: c5:c6 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c22 :: c7:c8:c9:c10 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c23 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c24 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c25 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c26 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c27 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
a__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
hole_c:c11_28 :: c:c1
hole_tt:0':s:U11:U12:plus:U21:U22:x2_28 :: tt:0':s:U11:U12:plus:U21:U22:x
hole_c2:c3:c43_28 :: c2:c3:c4
hole_c11:c12:c134_28 :: c11:c12:c13
hole_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c275_28 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
hole_c5:c66_28 :: c5:c6
hole_c7:c8:c9:c107_28 :: c7:c8:c9:c10
hole_c14:c15:c168_28 :: c14:c15:c16
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28 :: Nat -> tt:0':s:U11:U12:plus:U21:U22:x
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28 :: Nat -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27


Lemmas:
mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n128626_28)) -> gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n128626_28), rt in Omega(0)
a__U21(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n136054_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U22(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n155326_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)


Generator Equations:
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0) <=> tt
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(x))
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(0) <=> c25
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(+(x, 1)) <=> c17(c(c2(c11(c25), c25)), gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(x))


The following defined symbols remain to be analysed:
a__x, A__U11, A__U12, A__PLUS, mark, MARK, A__U21, A__U22, A__X, a__U11, a__U12, a__plus, a__U21

They will be analysed ascendingly in the following order:
A__U11 = A__U12
A__U11 = A__PLUS
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__U22
A__U11 = A__X
A__U12 = A__PLUS
mark < A__U12
A__U12 = MARK
A__U12 = A__U21
A__U12 = A__U22
A__U12 = A__X
A__PLUS = MARK
A__PLUS = A__U21
A__PLUS = A__U22
A__PLUS = A__X
mark < MARK
mark < A__U22
mark = a__x
mark = a__U11
mark = a__U12
mark = a__plus
mark = a__U21
mark = a__U22
MARK = A__U21
MARK = A__U22
MARK = A__X
A__U21 = A__U22
A__U21 = A__X
a__x < A__U22
A__U22 = A__X
a__x = a__U11
a__x = a__U12
a__x = a__plus
a__x = a__U21
a__x = a__U22
a__U11 = a__U12
a__U11 = a__plus
a__U11 = a__U21
a__U11 = a__U22
a__U12 = a__plus
a__U12 = a__U21
a__U12 = a__U22
a__plus = a__U21
a__plus = a__U22
a__U21 = a__U22

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

(21) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n174614_28))) -> *11_28, rt in Omega(0)

Induction Base:
a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, 0)))

Induction Step:
a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, +(n174614_28, 1)))) ->_R^Omega(0)
a__U21(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n174614_28)), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a)) ->_R^Omega(0)
a__U22(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n174614_28)), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a)) ->_R^Omega(0)
a__plus(a__x(mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a)), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n174614_28)))), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a))) ->_L^Omega(0)
a__plus(a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n174614_28)))), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a))) ->_L^Omega(0)
a__plus(a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n174614_28))), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a))) ->_IH
a__plus(*11_28, mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a))) ->_L^Omega(0)
a__plus(*11_28, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a))

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(22)
Obligation:
Innermost TRS:
Rules:
A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
A__U11(z0, z1, z2) -> c1
A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U12(z0, z1, z2) -> c4
A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
A__U21(z0, z1, z2) -> c6
A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U22(z0, z1, z2) -> c10
A__PLUS(z0, 0') -> c11(MARK(z0))
A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
A__PLUS(z0, z1) -> c13
A__X(z0, 0') -> c14
A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
A__X(z0, z1) -> c16
MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(tt) -> c25
MARK(s(z0)) -> c26(MARK(z0))
MARK(0') -> c27
a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
a__U11(z0, z1, z2) -> U11(z0, z1, z2)
a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U12(z0, z1, z2) -> U12(z0, z1, z2)
a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U22(z0, z1, z2) -> U22(z0, z1, z2)
a__plus(z0, 0') -> mark(z0)
a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> 0'
a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c:c1
tt :: tt:0':s:U11:U12:plus:U21:U22:x
c :: c2:c3:c4 -> c:c1
A__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c2:c3:c4
c1 :: c:c1
c2 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
A__PLUS :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c11:c12:c13
mark :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
MARK :: tt:0':s:U11:U12:plus:U21:U22:x -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c3 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
c4 :: c2:c3:c4
A__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c5:c6
c5 :: c7:c8:c9:c10 -> c5:c6
A__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c7:c8:c9:c10
c6 :: c5:c6
c7 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
a__x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
A__X :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c14:c15:c16
c8 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c9 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
0' :: tt:0':s:U11:U12:plus:U21:U22:x
c11 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c11:c12:c13
s :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c12 :: c:c1 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c14:c15:c16
c15 :: c5:c6 -> c14:c15:c16
c16 :: c14:c15:c16
U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c17 :: c:c1 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c18 :: c2:c3:c4 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c19 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c20 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c21 :: c5:c6 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c22 :: c7:c8:c9:c10 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c23 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c24 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c25 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c26 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c27 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
a__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
hole_c:c11_28 :: c:c1
hole_tt:0':s:U11:U12:plus:U21:U22:x2_28 :: tt:0':s:U11:U12:plus:U21:U22:x
hole_c2:c3:c43_28 :: c2:c3:c4
hole_c11:c12:c134_28 :: c11:c12:c13
hole_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c275_28 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
hole_c5:c66_28 :: c5:c6
hole_c7:c8:c9:c107_28 :: c7:c8:c9:c10
hole_c14:c15:c168_28 :: c14:c15:c16
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28 :: Nat -> tt:0':s:U11:U12:plus:U21:U22:x
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28 :: Nat -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27


Lemmas:
mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n128626_28)) -> gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n128626_28), rt in Omega(0)
a__U21(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n136054_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U22(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n155326_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n174614_28))) -> *11_28, rt in Omega(0)


Generator Equations:
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0) <=> tt
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(x))
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(0) <=> c25
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(+(x, 1)) <=> c17(c(c2(c11(c25), c25)), gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(x))


The following defined symbols remain to be analysed:
a__U11, A__U11, A__U12, A__PLUS, mark, MARK, A__U21, A__U22, A__X, a__U12, a__plus, a__U21, a__U22

They will be analysed ascendingly in the following order:
A__U11 = A__U12
A__U11 = A__PLUS
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__U22
A__U11 = A__X
A__U12 = A__PLUS
mark < A__U12
A__U12 = MARK
A__U12 = A__U21
A__U12 = A__U22
A__U12 = A__X
A__PLUS = MARK
A__PLUS = A__U21
A__PLUS = A__U22
A__PLUS = A__X
mark < MARK
mark < A__U22
mark = a__x
mark = a__U11
mark = a__U12
mark = a__plus
mark = a__U21
mark = a__U22
MARK = A__U21
MARK = A__U22
MARK = A__X
A__U21 = A__U22
A__U21 = A__X
a__x < A__U22
A__U22 = A__X
a__x = a__U11
a__x = a__U12
a__x = a__plus
a__x = a__U21
a__x = a__U22
a__U11 = a__U12
a__U11 = a__plus
a__U11 = a__U21
a__U11 = a__U22
a__U12 = a__plus
a__U12 = a__U21
a__U12 = a__U22
a__plus = a__U21
a__plus = a__U22
a__U21 = a__U22

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

(23) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
a__U11(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n195399_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)

Induction Base:
a__U11(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))

Induction Step:
a__U11(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(n195399_28, 1)), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) ->_R^Omega(0)
a__U12(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(n195399_28, 1)), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) ->_R^Omega(0)
s(a__plus(mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n195399_28))))) ->_L^Omega(0)
s(a__plus(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n195399_28))))) ->_L^Omega(0)
s(a__plus(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n195399_28)))) ->_R^Omega(0)
s(a__U11(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n195399_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_IH
s(*11_28)

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(24)
Obligation:
Innermost TRS:
Rules:
A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
A__U11(z0, z1, z2) -> c1
A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U12(z0, z1, z2) -> c4
A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
A__U21(z0, z1, z2) -> c6
A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U22(z0, z1, z2) -> c10
A__PLUS(z0, 0') -> c11(MARK(z0))
A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
A__PLUS(z0, z1) -> c13
A__X(z0, 0') -> c14
A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
A__X(z0, z1) -> c16
MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(tt) -> c25
MARK(s(z0)) -> c26(MARK(z0))
MARK(0') -> c27
a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
a__U11(z0, z1, z2) -> U11(z0, z1, z2)
a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U12(z0, z1, z2) -> U12(z0, z1, z2)
a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U22(z0, z1, z2) -> U22(z0, z1, z2)
a__plus(z0, 0') -> mark(z0)
a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> 0'
a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c:c1
tt :: tt:0':s:U11:U12:plus:U21:U22:x
c :: c2:c3:c4 -> c:c1
A__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c2:c3:c4
c1 :: c:c1
c2 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
A__PLUS :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c11:c12:c13
mark :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
MARK :: tt:0':s:U11:U12:plus:U21:U22:x -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c3 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
c4 :: c2:c3:c4
A__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c5:c6
c5 :: c7:c8:c9:c10 -> c5:c6
A__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c7:c8:c9:c10
c6 :: c5:c6
c7 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
a__x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
A__X :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c14:c15:c16
c8 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c9 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
0' :: tt:0':s:U11:U12:plus:U21:U22:x
c11 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c11:c12:c13
s :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c12 :: c:c1 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c14:c15:c16
c15 :: c5:c6 -> c14:c15:c16
c16 :: c14:c15:c16
U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c17 :: c:c1 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c18 :: c2:c3:c4 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c19 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c20 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c21 :: c5:c6 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c22 :: c7:c8:c9:c10 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c23 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c24 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c25 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c26 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c27 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
a__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
hole_c:c11_28 :: c:c1
hole_tt:0':s:U11:U12:plus:U21:U22:x2_28 :: tt:0':s:U11:U12:plus:U21:U22:x
hole_c2:c3:c43_28 :: c2:c3:c4
hole_c11:c12:c134_28 :: c11:c12:c13
hole_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c275_28 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
hole_c5:c66_28 :: c5:c6
hole_c7:c8:c9:c107_28 :: c7:c8:c9:c10
hole_c14:c15:c168_28 :: c14:c15:c16
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28 :: Nat -> tt:0':s:U11:U12:plus:U21:U22:x
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28 :: Nat -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27


Lemmas:
mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n128626_28)) -> gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n128626_28), rt in Omega(0)
a__U21(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n136054_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U22(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n155326_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n174614_28))) -> *11_28, rt in Omega(0)
a__U11(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n195399_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)


Generator Equations:
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0) <=> tt
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(x))
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(0) <=> c25
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(+(x, 1)) <=> c17(c(c2(c11(c25), c25)), gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(x))


The following defined symbols remain to be analysed:
a__U12, A__U11, A__U12, A__PLUS, mark, MARK, A__U21, A__U22, a__x, A__X, a__plus, a__U21, a__U22

They will be analysed ascendingly in the following order:
A__U11 = A__U12
A__U11 = A__PLUS
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__U22
A__U11 = A__X
A__U12 = A__PLUS
mark < A__U12
A__U12 = MARK
A__U12 = A__U21
A__U12 = A__U22
A__U12 = A__X
A__PLUS = MARK
A__PLUS = A__U21
A__PLUS = A__U22
A__PLUS = A__X
mark < MARK
mark < A__U22
mark = a__x
mark = a__U11
mark = a__U12
mark = a__plus
mark = a__U21
mark = a__U22
MARK = A__U21
MARK = A__U22
MARK = A__X
A__U21 = A__U22
A__U21 = A__X
a__x < A__U22
A__U22 = A__X
a__x = a__U11
a__x = a__U12
a__x = a__plus
a__x = a__U21
a__x = a__U22
a__U11 = a__U12
a__U11 = a__plus
a__U11 = a__U21
a__U11 = a__U22
a__U12 = a__plus
a__U12 = a__U21
a__U12 = a__U22
a__plus = a__U21
a__plus = a__U22
a__U21 = a__U22

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

(25) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
a__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n204288_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)

Induction Base:
a__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))

Induction Step:
a__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(n204288_28, 1)), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) ->_R^Omega(0)
s(a__plus(mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(n204288_28, 1))))) ->_L^Omega(0)
s(a__plus(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n204288_28))))) ->_L^Omega(0)
s(a__plus(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n204288_28)))) ->_R^Omega(0)
s(a__U11(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n204288_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_R^Omega(0)
s(a__U12(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n204288_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_IH
s(*11_28)

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(26)
Obligation:
Innermost TRS:
Rules:
A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
A__U11(z0, z1, z2) -> c1
A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U12(z0, z1, z2) -> c4
A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
A__U21(z0, z1, z2) -> c6
A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U22(z0, z1, z2) -> c10
A__PLUS(z0, 0') -> c11(MARK(z0))
A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
A__PLUS(z0, z1) -> c13
A__X(z0, 0') -> c14
A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
A__X(z0, z1) -> c16
MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(tt) -> c25
MARK(s(z0)) -> c26(MARK(z0))
MARK(0') -> c27
a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
a__U11(z0, z1, z2) -> U11(z0, z1, z2)
a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U12(z0, z1, z2) -> U12(z0, z1, z2)
a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U22(z0, z1, z2) -> U22(z0, z1, z2)
a__plus(z0, 0') -> mark(z0)
a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> 0'
a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c:c1
tt :: tt:0':s:U11:U12:plus:U21:U22:x
c :: c2:c3:c4 -> c:c1
A__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c2:c3:c4
c1 :: c:c1
c2 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
A__PLUS :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c11:c12:c13
mark :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
MARK :: tt:0':s:U11:U12:plus:U21:U22:x -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c3 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
c4 :: c2:c3:c4
A__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c5:c6
c5 :: c7:c8:c9:c10 -> c5:c6
A__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c7:c8:c9:c10
c6 :: c5:c6
c7 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
a__x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
A__X :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c14:c15:c16
c8 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c9 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
0' :: tt:0':s:U11:U12:plus:U21:U22:x
c11 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c11:c12:c13
s :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c12 :: c:c1 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c14:c15:c16
c15 :: c5:c6 -> c14:c15:c16
c16 :: c14:c15:c16
U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c17 :: c:c1 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c18 :: c2:c3:c4 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c19 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c20 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c21 :: c5:c6 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c22 :: c7:c8:c9:c10 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c23 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c24 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c25 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c26 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c27 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
a__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
hole_c:c11_28 :: c:c1
hole_tt:0':s:U11:U12:plus:U21:U22:x2_28 :: tt:0':s:U11:U12:plus:U21:U22:x
hole_c2:c3:c43_28 :: c2:c3:c4
hole_c11:c12:c134_28 :: c11:c12:c13
hole_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c275_28 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
hole_c5:c66_28 :: c5:c6
hole_c7:c8:c9:c107_28 :: c7:c8:c9:c10
hole_c14:c15:c168_28 :: c14:c15:c16
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28 :: Nat -> tt:0':s:U11:U12:plus:U21:U22:x
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28 :: Nat -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27


Lemmas:
mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n128626_28)) -> gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n128626_28), rt in Omega(0)
a__U21(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n136054_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U22(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n155326_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n174614_28))) -> *11_28, rt in Omega(0)
a__U11(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n195399_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n204288_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)


Generator Equations:
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0) <=> tt
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(x))
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(0) <=> c25
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(+(x, 1)) <=> c17(c(c2(c11(c25), c25)), gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(x))


The following defined symbols remain to be analysed:
a__plus, A__U11, A__U12, A__PLUS, mark, MARK, A__U21, A__U22, a__x, A__X, a__U11, a__U21, a__U22

They will be analysed ascendingly in the following order:
A__U11 = A__U12
A__U11 = A__PLUS
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__U22
A__U11 = A__X
A__U12 = A__PLUS
mark < A__U12
A__U12 = MARK
A__U12 = A__U21
A__U12 = A__U22
A__U12 = A__X
A__PLUS = MARK
A__PLUS = A__U21
A__PLUS = A__U22
A__PLUS = A__X
mark < MARK
mark < A__U22
mark = a__x
mark = a__U11
mark = a__U12
mark = a__plus
mark = a__U21
mark = a__U22
MARK = A__U21
MARK = A__U22
MARK = A__X
A__U21 = A__U22
A__U21 = A__X
a__x < A__U22
A__U22 = A__X
a__x = a__U11
a__x = a__U12
a__x = a__plus
a__x = a__U21
a__x = a__U22
a__U11 = a__U12
a__U11 = a__plus
a__U11 = a__U21
a__U11 = a__U22
a__U12 = a__plus
a__U12 = a__U21
a__U12 = a__U22
a__plus = a__U21
a__plus = a__U22
a__U21 = a__U22

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

(27) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
a__plus(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n212992_28))) -> *11_28, rt in Omega(0)

Induction Base:
a__plus(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, 0)))

Induction Step:
a__plus(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, +(n212992_28, 1)))) ->_R^Omega(0)
a__U11(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n212992_28)), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a)) ->_R^Omega(0)
a__U12(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n212992_28)), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a)) ->_R^Omega(0)
s(a__plus(mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a)), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n212992_28))))) ->_L^Omega(0)
s(a__plus(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n212992_28))))) ->_L^Omega(0)
s(a__plus(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n212992_28)))) ->_IH
s(*11_28)

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(28)
Obligation:
Innermost TRS:
Rules:
A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
A__U11(z0, z1, z2) -> c1
A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U12(z0, z1, z2) -> c4
A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
A__U21(z0, z1, z2) -> c6
A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U22(z0, z1, z2) -> c10
A__PLUS(z0, 0') -> c11(MARK(z0))
A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
A__PLUS(z0, z1) -> c13
A__X(z0, 0') -> c14
A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
A__X(z0, z1) -> c16
MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(tt) -> c25
MARK(s(z0)) -> c26(MARK(z0))
MARK(0') -> c27
a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
a__U11(z0, z1, z2) -> U11(z0, z1, z2)
a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U12(z0, z1, z2) -> U12(z0, z1, z2)
a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U22(z0, z1, z2) -> U22(z0, z1, z2)
a__plus(z0, 0') -> mark(z0)
a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> 0'
a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c:c1
tt :: tt:0':s:U11:U12:plus:U21:U22:x
c :: c2:c3:c4 -> c:c1
A__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c2:c3:c4
c1 :: c:c1
c2 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
A__PLUS :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c11:c12:c13
mark :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
MARK :: tt:0':s:U11:U12:plus:U21:U22:x -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c3 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
c4 :: c2:c3:c4
A__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c5:c6
c5 :: c7:c8:c9:c10 -> c5:c6
A__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c7:c8:c9:c10
c6 :: c5:c6
c7 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
a__x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
A__X :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c14:c15:c16
c8 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c9 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
0' :: tt:0':s:U11:U12:plus:U21:U22:x
c11 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c11:c12:c13
s :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c12 :: c:c1 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c14:c15:c16
c15 :: c5:c6 -> c14:c15:c16
c16 :: c14:c15:c16
U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c17 :: c:c1 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c18 :: c2:c3:c4 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c19 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c20 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c21 :: c5:c6 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c22 :: c7:c8:c9:c10 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c23 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c24 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c25 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c26 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c27 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
a__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
hole_c:c11_28 :: c:c1
hole_tt:0':s:U11:U12:plus:U21:U22:x2_28 :: tt:0':s:U11:U12:plus:U21:U22:x
hole_c2:c3:c43_28 :: c2:c3:c4
hole_c11:c12:c134_28 :: c11:c12:c13
hole_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c275_28 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
hole_c5:c66_28 :: c5:c6
hole_c7:c8:c9:c107_28 :: c7:c8:c9:c10
hole_c14:c15:c168_28 :: c14:c15:c16
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28 :: Nat -> tt:0':s:U11:U12:plus:U21:U22:x
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28 :: Nat -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27


Lemmas:
mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n128626_28)) -> gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n128626_28), rt in Omega(0)
a__U21(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n136054_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U22(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n155326_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n174614_28))) -> *11_28, rt in Omega(0)
a__U11(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n195399_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n204288_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__plus(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n212992_28))) -> *11_28, rt in Omega(0)


Generator Equations:
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0) <=> tt
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(x))
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(0) <=> c25
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(+(x, 1)) <=> c17(c(c2(c11(c25), c25)), gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(x))


The following defined symbols remain to be analysed:
mark, A__U11, A__U12, A__PLUS, MARK, A__U21, A__U22, a__x, A__X, a__U11, a__U12, a__U21, a__U22

They will be analysed ascendingly in the following order:
A__U11 = A__U12
A__U11 = A__PLUS
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__U22
A__U11 = A__X
A__U12 = A__PLUS
mark < A__U12
A__U12 = MARK
A__U12 = A__U21
A__U12 = A__U22
A__U12 = A__X
A__PLUS = MARK
A__PLUS = A__U21
A__PLUS = A__U22
A__PLUS = A__X
mark < MARK
mark < A__U22
mark = a__x
mark = a__U11
mark = a__U12
mark = a__plus
mark = a__U21
mark = a__U22
MARK = A__U21
MARK = A__U22
MARK = A__X
A__U21 = A__U22
A__U21 = A__X
a__x < A__U22
A__U22 = A__X
a__x = a__U11
a__x = a__U12
a__x = a__plus
a__x = a__U21
a__x = a__U22
a__U11 = a__U12
a__U11 = a__plus
a__U11 = a__U21
a__U11 = a__U22
a__U12 = a__plus
a__U12 = a__U21
a__U12 = a__U22
a__plus = a__U21
a__plus = a__U22
a__U21 = a__U22

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

(29) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28)) -> gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28), rt in Omega(0)

Induction Base:
mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0)) ->_R^Omega(0)
tt

Induction Step:
mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(n223086_28, 1))) ->_R^Omega(0)
s(mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28))) ->_IH
s(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c223087_28))

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(30)
Obligation:
Innermost TRS:
Rules:
A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
A__U11(z0, z1, z2) -> c1
A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U12(z0, z1, z2) -> c4
A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
A__U21(z0, z1, z2) -> c6
A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U22(z0, z1, z2) -> c10
A__PLUS(z0, 0') -> c11(MARK(z0))
A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
A__PLUS(z0, z1) -> c13
A__X(z0, 0') -> c14
A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
A__X(z0, z1) -> c16
MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(tt) -> c25
MARK(s(z0)) -> c26(MARK(z0))
MARK(0') -> c27
a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
a__U11(z0, z1, z2) -> U11(z0, z1, z2)
a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U12(z0, z1, z2) -> U12(z0, z1, z2)
a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U22(z0, z1, z2) -> U22(z0, z1, z2)
a__plus(z0, 0') -> mark(z0)
a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> 0'
a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c:c1
tt :: tt:0':s:U11:U12:plus:U21:U22:x
c :: c2:c3:c4 -> c:c1
A__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c2:c3:c4
c1 :: c:c1
c2 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
A__PLUS :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c11:c12:c13
mark :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
MARK :: tt:0':s:U11:U12:plus:U21:U22:x -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c3 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
c4 :: c2:c3:c4
A__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c5:c6
c5 :: c7:c8:c9:c10 -> c5:c6
A__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c7:c8:c9:c10
c6 :: c5:c6
c7 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
a__x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
A__X :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c14:c15:c16
c8 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c9 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
0' :: tt:0':s:U11:U12:plus:U21:U22:x
c11 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c11:c12:c13
s :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c12 :: c:c1 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c14:c15:c16
c15 :: c5:c6 -> c14:c15:c16
c16 :: c14:c15:c16
U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c17 :: c:c1 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c18 :: c2:c3:c4 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c19 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c20 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c21 :: c5:c6 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c22 :: c7:c8:c9:c10 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c23 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c24 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c25 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c26 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c27 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
a__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
hole_c:c11_28 :: c:c1
hole_tt:0':s:U11:U12:plus:U21:U22:x2_28 :: tt:0':s:U11:U12:plus:U21:U22:x
hole_c2:c3:c43_28 :: c2:c3:c4
hole_c11:c12:c134_28 :: c11:c12:c13
hole_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c275_28 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
hole_c5:c66_28 :: c5:c6
hole_c7:c8:c9:c107_28 :: c7:c8:c9:c10
hole_c14:c15:c168_28 :: c14:c15:c16
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28 :: Nat -> tt:0':s:U11:U12:plus:U21:U22:x
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28 :: Nat -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27


Lemmas:
mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28)) -> gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28), rt in Omega(0)
a__U21(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n136054_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U22(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n155326_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n174614_28))) -> *11_28, rt in Omega(0)
a__U11(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n195399_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n204288_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__plus(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n212992_28))) -> *11_28, rt in Omega(0)


Generator Equations:
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0) <=> tt
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(x))
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(0) <=> c25
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(+(x, 1)) <=> c17(c(c2(c11(c25), c25)), gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(x))


The following defined symbols remain to be analysed:
a__U21, A__U11, A__U12, A__PLUS, MARK, A__U21, A__U22, a__x, A__X, a__U11, a__U12, a__U22

They will be analysed ascendingly in the following order:
A__U11 = A__U12
A__U11 = A__PLUS
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__U22
A__U11 = A__X
A__U12 = A__PLUS
mark < A__U12
A__U12 = MARK
A__U12 = A__U21
A__U12 = A__U22
A__U12 = A__X
A__PLUS = MARK
A__PLUS = A__U21
A__PLUS = A__U22
A__PLUS = A__X
mark < MARK
mark < A__U22
mark = a__x
mark = a__U11
mark = a__U12
mark = a__plus
mark = a__U21
mark = a__U22
MARK = A__U21
MARK = A__U22
MARK = A__X
A__U21 = A__U22
A__U21 = A__X
a__x < A__U22
A__U22 = A__X
a__x = a__U11
a__x = a__U12
a__x = a__plus
a__x = a__U21
a__x = a__U22
a__U11 = a__U12
a__U11 = a__plus
a__U11 = a__U21
a__U11 = a__U22
a__U12 = a__plus
a__U12 = a__U21
a__U12 = a__U22
a__plus = a__U21
a__plus = a__U22
a__U21 = a__U22

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

(31) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
a__U21(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n231132_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)

Induction Base:
a__U21(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))

Induction Step:
a__U21(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(n231132_28, 1)), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) ->_R^Omega(0)
a__U22(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(n231132_28, 1)), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) ->_R^Omega(0)
a__plus(a__x(mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n231132_28)))), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_L^Omega(0)
a__plus(a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n231132_28)))), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_L^Omega(0)
a__plus(a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n231132_28))), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_R^Omega(0)
a__plus(a__U21(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n231132_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_IH
a__plus(*11_28, mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_L^Omega(0)
a__plus(*11_28, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(32)
Obligation:
Innermost TRS:
Rules:
A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
A__U11(z0, z1, z2) -> c1
A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U12(z0, z1, z2) -> c4
A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
A__U21(z0, z1, z2) -> c6
A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U22(z0, z1, z2) -> c10
A__PLUS(z0, 0') -> c11(MARK(z0))
A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
A__PLUS(z0, z1) -> c13
A__X(z0, 0') -> c14
A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
A__X(z0, z1) -> c16
MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(tt) -> c25
MARK(s(z0)) -> c26(MARK(z0))
MARK(0') -> c27
a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
a__U11(z0, z1, z2) -> U11(z0, z1, z2)
a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U12(z0, z1, z2) -> U12(z0, z1, z2)
a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U22(z0, z1, z2) -> U22(z0, z1, z2)
a__plus(z0, 0') -> mark(z0)
a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> 0'
a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c:c1
tt :: tt:0':s:U11:U12:plus:U21:U22:x
c :: c2:c3:c4 -> c:c1
A__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c2:c3:c4
c1 :: c:c1
c2 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
A__PLUS :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c11:c12:c13
mark :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
MARK :: tt:0':s:U11:U12:plus:U21:U22:x -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c3 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
c4 :: c2:c3:c4
A__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c5:c6
c5 :: c7:c8:c9:c10 -> c5:c6
A__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c7:c8:c9:c10
c6 :: c5:c6
c7 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
a__x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
A__X :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c14:c15:c16
c8 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c9 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
0' :: tt:0':s:U11:U12:plus:U21:U22:x
c11 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c11:c12:c13
s :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c12 :: c:c1 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c14:c15:c16
c15 :: c5:c6 -> c14:c15:c16
c16 :: c14:c15:c16
U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c17 :: c:c1 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c18 :: c2:c3:c4 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c19 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c20 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c21 :: c5:c6 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c22 :: c7:c8:c9:c10 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c23 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c24 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c25 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c26 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c27 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
a__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
hole_c:c11_28 :: c:c1
hole_tt:0':s:U11:U12:plus:U21:U22:x2_28 :: tt:0':s:U11:U12:plus:U21:U22:x
hole_c2:c3:c43_28 :: c2:c3:c4
hole_c11:c12:c134_28 :: c11:c12:c13
hole_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c275_28 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
hole_c5:c66_28 :: c5:c6
hole_c7:c8:c9:c107_28 :: c7:c8:c9:c10
hole_c14:c15:c168_28 :: c14:c15:c16
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28 :: Nat -> tt:0':s:U11:U12:plus:U21:U22:x
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28 :: Nat -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27


Lemmas:
mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28)) -> gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28), rt in Omega(0)
a__U21(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n231132_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U22(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n155326_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n174614_28))) -> *11_28, rt in Omega(0)
a__U11(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n195399_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n204288_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__plus(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n212992_28))) -> *11_28, rt in Omega(0)


Generator Equations:
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0) <=> tt
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(x))
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(0) <=> c25
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(+(x, 1)) <=> c17(c(c2(c11(c25), c25)), gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(x))


The following defined symbols remain to be analysed:
a__U22, A__U11, A__U12, A__PLUS, MARK, A__U21, A__U22, a__x, A__X, a__U11, a__U12

They will be analysed ascendingly in the following order:
A__U11 = A__U12
A__U11 = A__PLUS
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__U22
A__U11 = A__X
A__U12 = A__PLUS
mark < A__U12
A__U12 = MARK
A__U12 = A__U21
A__U12 = A__U22
A__U12 = A__X
A__PLUS = MARK
A__PLUS = A__U21
A__PLUS = A__U22
A__PLUS = A__X
mark < MARK
mark < A__U22
mark = a__x
mark = a__U11
mark = a__U12
mark = a__plus
mark = a__U21
mark = a__U22
MARK = A__U21
MARK = A__U22
MARK = A__X
A__U21 = A__U22
A__U21 = A__X
a__x < A__U22
A__U22 = A__X
a__x = a__U11
a__x = a__U12
a__x = a__plus
a__x = a__U21
a__x = a__U22
a__U11 = a__U12
a__U11 = a__plus
a__U11 = a__U21
a__U11 = a__U22
a__U12 = a__plus
a__U12 = a__U21
a__U12 = a__U22
a__plus = a__U21
a__plus = a__U22
a__U21 = a__U22

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

(33) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
a__U22(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n253794_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)

Induction Base:
a__U22(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))

Induction Step:
a__U22(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(n253794_28, 1)), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) ->_R^Omega(0)
a__plus(a__x(mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(n253794_28, 1)))), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_L^Omega(0)
a__plus(a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n253794_28)))), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_L^Omega(0)
a__plus(a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n253794_28))), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_R^Omega(0)
a__plus(a__U21(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n253794_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_R^Omega(0)
a__plus(a__U22(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n253794_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_IH
a__plus(*11_28, mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_L^Omega(0)
a__plus(*11_28, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(34)
Obligation:
Innermost TRS:
Rules:
A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
A__U11(z0, z1, z2) -> c1
A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U12(z0, z1, z2) -> c4
A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
A__U21(z0, z1, z2) -> c6
A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U22(z0, z1, z2) -> c10
A__PLUS(z0, 0') -> c11(MARK(z0))
A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
A__PLUS(z0, z1) -> c13
A__X(z0, 0') -> c14
A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
A__X(z0, z1) -> c16
MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(tt) -> c25
MARK(s(z0)) -> c26(MARK(z0))
MARK(0') -> c27
a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
a__U11(z0, z1, z2) -> U11(z0, z1, z2)
a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U12(z0, z1, z2) -> U12(z0, z1, z2)
a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U22(z0, z1, z2) -> U22(z0, z1, z2)
a__plus(z0, 0') -> mark(z0)
a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> 0'
a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c:c1
tt :: tt:0':s:U11:U12:plus:U21:U22:x
c :: c2:c3:c4 -> c:c1
A__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c2:c3:c4
c1 :: c:c1
c2 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
A__PLUS :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c11:c12:c13
mark :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
MARK :: tt:0':s:U11:U12:plus:U21:U22:x -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c3 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
c4 :: c2:c3:c4
A__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c5:c6
c5 :: c7:c8:c9:c10 -> c5:c6
A__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c7:c8:c9:c10
c6 :: c5:c6
c7 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
a__x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
A__X :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c14:c15:c16
c8 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c9 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
0' :: tt:0':s:U11:U12:plus:U21:U22:x
c11 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c11:c12:c13
s :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c12 :: c:c1 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c14:c15:c16
c15 :: c5:c6 -> c14:c15:c16
c16 :: c14:c15:c16
U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c17 :: c:c1 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c18 :: c2:c3:c4 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c19 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c20 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c21 :: c5:c6 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c22 :: c7:c8:c9:c10 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c23 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c24 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c25 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c26 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c27 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
a__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
hole_c:c11_28 :: c:c1
hole_tt:0':s:U11:U12:plus:U21:U22:x2_28 :: tt:0':s:U11:U12:plus:U21:U22:x
hole_c2:c3:c43_28 :: c2:c3:c4
hole_c11:c12:c134_28 :: c11:c12:c13
hole_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c275_28 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
hole_c5:c66_28 :: c5:c6
hole_c7:c8:c9:c107_28 :: c7:c8:c9:c10
hole_c14:c15:c168_28 :: c14:c15:c16
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28 :: Nat -> tt:0':s:U11:U12:plus:U21:U22:x
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28 :: Nat -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27


Lemmas:
mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28)) -> gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28), rt in Omega(0)
a__U21(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n231132_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U22(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n253794_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n174614_28))) -> *11_28, rt in Omega(0)
a__U11(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n195399_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n204288_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__plus(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n212992_28))) -> *11_28, rt in Omega(0)


Generator Equations:
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0) <=> tt
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(x))
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(0) <=> c25
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(+(x, 1)) <=> c17(c(c2(c11(c25), c25)), gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(x))


The following defined symbols remain to be analysed:
a__x, A__U11, A__U12, A__PLUS, MARK, A__U21, A__U22, A__X, a__U11, a__U12

They will be analysed ascendingly in the following order:
A__U11 = A__U12
A__U11 = A__PLUS
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__U22
A__U11 = A__X
A__U12 = A__PLUS
mark < A__U12
A__U12 = MARK
A__U12 = A__U21
A__U12 = A__U22
A__U12 = A__X
A__PLUS = MARK
A__PLUS = A__U21
A__PLUS = A__U22
A__PLUS = A__X
mark < MARK
mark < A__U22
mark = a__x
mark = a__U11
mark = a__U12
mark = a__plus
mark = a__U21
mark = a__U22
MARK = A__U21
MARK = A__U22
MARK = A__X
A__U21 = A__U22
A__U21 = A__X
a__x < A__U22
A__U22 = A__X
a__x = a__U11
a__x = a__U12
a__x = a__plus
a__x = a__U21
a__x = a__U22
a__U11 = a__U12
a__U11 = a__plus
a__U11 = a__U21
a__U11 = a__U22
a__U12 = a__plus
a__U12 = a__U21
a__U12 = a__U22
a__plus = a__U21
a__plus = a__U22
a__U21 = a__U22

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

(35) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n275862_28))) -> *11_28, rt in Omega(0)

Induction Base:
a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, 0)))

Induction Step:
a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, +(n275862_28, 1)))) ->_R^Omega(0)
a__U21(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n275862_28)), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a)) ->_R^Omega(0)
a__U22(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n275862_28)), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a)) ->_R^Omega(0)
a__plus(a__x(mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a)), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n275862_28)))), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a))) ->_L^Omega(0)
a__plus(a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n275862_28)))), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a))) ->_L^Omega(0)
a__plus(a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n275862_28))), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a))) ->_IH
a__plus(*11_28, mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a))) ->_L^Omega(0)
a__plus(*11_28, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a))

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(36)
Obligation:
Innermost TRS:
Rules:
A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
A__U11(z0, z1, z2) -> c1
A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U12(z0, z1, z2) -> c4
A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
A__U21(z0, z1, z2) -> c6
A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U22(z0, z1, z2) -> c10
A__PLUS(z0, 0') -> c11(MARK(z0))
A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
A__PLUS(z0, z1) -> c13
A__X(z0, 0') -> c14
A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
A__X(z0, z1) -> c16
MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(tt) -> c25
MARK(s(z0)) -> c26(MARK(z0))
MARK(0') -> c27
a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
a__U11(z0, z1, z2) -> U11(z0, z1, z2)
a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U12(z0, z1, z2) -> U12(z0, z1, z2)
a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U22(z0, z1, z2) -> U22(z0, z1, z2)
a__plus(z0, 0') -> mark(z0)
a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> 0'
a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c:c1
tt :: tt:0':s:U11:U12:plus:U21:U22:x
c :: c2:c3:c4 -> c:c1
A__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c2:c3:c4
c1 :: c:c1
c2 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
A__PLUS :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c11:c12:c13
mark :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
MARK :: tt:0':s:U11:U12:plus:U21:U22:x -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c3 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
c4 :: c2:c3:c4
A__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c5:c6
c5 :: c7:c8:c9:c10 -> c5:c6
A__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c7:c8:c9:c10
c6 :: c5:c6
c7 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
a__x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
A__X :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c14:c15:c16
c8 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c9 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
0' :: tt:0':s:U11:U12:plus:U21:U22:x
c11 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c11:c12:c13
s :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c12 :: c:c1 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c14:c15:c16
c15 :: c5:c6 -> c14:c15:c16
c16 :: c14:c15:c16
U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c17 :: c:c1 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c18 :: c2:c3:c4 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c19 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c20 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c21 :: c5:c6 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c22 :: c7:c8:c9:c10 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c23 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c24 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c25 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c26 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c27 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
a__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
hole_c:c11_28 :: c:c1
hole_tt:0':s:U11:U12:plus:U21:U22:x2_28 :: tt:0':s:U11:U12:plus:U21:U22:x
hole_c2:c3:c43_28 :: c2:c3:c4
hole_c11:c12:c134_28 :: c11:c12:c13
hole_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c275_28 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
hole_c5:c66_28 :: c5:c6
hole_c7:c8:c9:c107_28 :: c7:c8:c9:c10
hole_c14:c15:c168_28 :: c14:c15:c16
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28 :: Nat -> tt:0':s:U11:U12:plus:U21:U22:x
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28 :: Nat -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27


Lemmas:
mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28)) -> gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28), rt in Omega(0)
a__U21(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n231132_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U22(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n253794_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n275862_28))) -> *11_28, rt in Omega(0)
a__U11(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n195399_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n204288_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__plus(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n212992_28))) -> *11_28, rt in Omega(0)


Generator Equations:
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0) <=> tt
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(x))
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(0) <=> c25
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(+(x, 1)) <=> c17(c(c2(c11(c25), c25)), gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(x))


The following defined symbols remain to be analysed:
a__U11, A__U11, A__U12, A__PLUS, MARK, A__U21, A__U22, A__X, a__U12

They will be analysed ascendingly in the following order:
A__U11 = A__U12
A__U11 = A__PLUS
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__U22
A__U11 = A__X
A__U12 = A__PLUS
mark < A__U12
A__U12 = MARK
A__U12 = A__U21
A__U12 = A__U22
A__U12 = A__X
A__PLUS = MARK
A__PLUS = A__U21
A__PLUS = A__U22
A__PLUS = A__X
mark < MARK
mark < A__U22
mark = a__x
mark = a__U11
mark = a__U12
mark = a__plus
mark = a__U21
mark = a__U22
MARK = A__U21
MARK = A__U22
MARK = A__X
A__U21 = A__U22
A__U21 = A__X
a__x < A__U22
A__U22 = A__X
a__x = a__U11
a__x = a__U12
a__x = a__plus
a__x = a__U21
a__x = a__U22
a__U11 = a__U12
a__U11 = a__plus
a__U11 = a__U21
a__U11 = a__U22
a__U12 = a__plus
a__U12 = a__U21
a__U12 = a__U22
a__plus = a__U21
a__plus = a__U22
a__U21 = a__U22

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

(37) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
a__U11(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n298923_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)

Induction Base:
a__U11(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))

Induction Step:
a__U11(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(n298923_28, 1)), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) ->_R^Omega(0)
a__U12(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(n298923_28, 1)), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) ->_R^Omega(0)
s(a__plus(mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n298923_28))))) ->_L^Omega(0)
s(a__plus(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n298923_28))))) ->_L^Omega(0)
s(a__plus(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n298923_28)))) ->_R^Omega(0)
s(a__U11(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n298923_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_IH
s(*11_28)

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(38)
Obligation:
Innermost TRS:
Rules:
A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
A__U11(z0, z1, z2) -> c1
A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U12(z0, z1, z2) -> c4
A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
A__U21(z0, z1, z2) -> c6
A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U22(z0, z1, z2) -> c10
A__PLUS(z0, 0') -> c11(MARK(z0))
A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
A__PLUS(z0, z1) -> c13
A__X(z0, 0') -> c14
A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
A__X(z0, z1) -> c16
MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(tt) -> c25
MARK(s(z0)) -> c26(MARK(z0))
MARK(0') -> c27
a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
a__U11(z0, z1, z2) -> U11(z0, z1, z2)
a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U12(z0, z1, z2) -> U12(z0, z1, z2)
a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U22(z0, z1, z2) -> U22(z0, z1, z2)
a__plus(z0, 0') -> mark(z0)
a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> 0'
a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c:c1
tt :: tt:0':s:U11:U12:plus:U21:U22:x
c :: c2:c3:c4 -> c:c1
A__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c2:c3:c4
c1 :: c:c1
c2 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
A__PLUS :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c11:c12:c13
mark :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
MARK :: tt:0':s:U11:U12:plus:U21:U22:x -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c3 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
c4 :: c2:c3:c4
A__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c5:c6
c5 :: c7:c8:c9:c10 -> c5:c6
A__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c7:c8:c9:c10
c6 :: c5:c6
c7 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
a__x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
A__X :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c14:c15:c16
c8 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c9 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
0' :: tt:0':s:U11:U12:plus:U21:U22:x
c11 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c11:c12:c13
s :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c12 :: c:c1 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c14:c15:c16
c15 :: c5:c6 -> c14:c15:c16
c16 :: c14:c15:c16
U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c17 :: c:c1 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c18 :: c2:c3:c4 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c19 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c20 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c21 :: c5:c6 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c22 :: c7:c8:c9:c10 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c23 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c24 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c25 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c26 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c27 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
a__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
hole_c:c11_28 :: c:c1
hole_tt:0':s:U11:U12:plus:U21:U22:x2_28 :: tt:0':s:U11:U12:plus:U21:U22:x
hole_c2:c3:c43_28 :: c2:c3:c4
hole_c11:c12:c134_28 :: c11:c12:c13
hole_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c275_28 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
hole_c5:c66_28 :: c5:c6
hole_c7:c8:c9:c107_28 :: c7:c8:c9:c10
hole_c14:c15:c168_28 :: c14:c15:c16
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28 :: Nat -> tt:0':s:U11:U12:plus:U21:U22:x
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28 :: Nat -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27


Lemmas:
mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28)) -> gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28), rt in Omega(0)
a__U21(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n231132_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U22(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n253794_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n275862_28))) -> *11_28, rt in Omega(0)
a__U11(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n298923_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n204288_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__plus(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n212992_28))) -> *11_28, rt in Omega(0)


Generator Equations:
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0) <=> tt
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(x))
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(0) <=> c25
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(+(x, 1)) <=> c17(c(c2(c11(c25), c25)), gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(x))


The following defined symbols remain to be analysed:
a__U12, A__U11, A__U12, A__PLUS, MARK, A__U21, A__U22, A__X

They will be analysed ascendingly in the following order:
A__U11 = A__U12
A__U11 = A__PLUS
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__U22
A__U11 = A__X
A__U12 = A__PLUS
mark < A__U12
A__U12 = MARK
A__U12 = A__U21
A__U12 = A__U22
A__U12 = A__X
A__PLUS = MARK
A__PLUS = A__U21
A__PLUS = A__U22
A__PLUS = A__X
mark < MARK
mark < A__U22
mark = a__x
mark = a__U11
mark = a__U12
mark = a__plus
mark = a__U21
mark = a__U22
MARK = A__U21
MARK = A__U22
MARK = A__X
A__U21 = A__U22
A__U21 = A__X
a__x < A__U22
A__U22 = A__X
a__x = a__U11
a__x = a__U12
a__x = a__plus
a__x = a__U21
a__x = a__U22
a__U11 = a__U12
a__U11 = a__plus
a__U11 = a__U21
a__U11 = a__U22
a__U12 = a__plus
a__U12 = a__U21
a__U12 = a__U22
a__plus = a__U21
a__plus = a__U22
a__U21 = a__U22

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

(39) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
a__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n309027_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)

Induction Base:
a__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))

Induction Step:
a__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(n309027_28, 1)), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) ->_R^Omega(0)
s(a__plus(mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(n309027_28, 1))))) ->_L^Omega(0)
s(a__plus(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n309027_28))))) ->_L^Omega(0)
s(a__plus(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n309027_28)))) ->_R^Omega(0)
s(a__U11(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n309027_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_R^Omega(0)
s(a__U12(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n309027_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_IH
s(*11_28)

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(40)
Obligation:
Innermost TRS:
Rules:
A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
A__U11(z0, z1, z2) -> c1
A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U12(z0, z1, z2) -> c4
A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
A__U21(z0, z1, z2) -> c6
A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U22(z0, z1, z2) -> c10
A__PLUS(z0, 0') -> c11(MARK(z0))
A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
A__PLUS(z0, z1) -> c13
A__X(z0, 0') -> c14
A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
A__X(z0, z1) -> c16
MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(tt) -> c25
MARK(s(z0)) -> c26(MARK(z0))
MARK(0') -> c27
a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
a__U11(z0, z1, z2) -> U11(z0, z1, z2)
a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U12(z0, z1, z2) -> U12(z0, z1, z2)
a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U22(z0, z1, z2) -> U22(z0, z1, z2)
a__plus(z0, 0') -> mark(z0)
a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> 0'
a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c:c1
tt :: tt:0':s:U11:U12:plus:U21:U22:x
c :: c2:c3:c4 -> c:c1
A__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c2:c3:c4
c1 :: c:c1
c2 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
A__PLUS :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c11:c12:c13
mark :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
MARK :: tt:0':s:U11:U12:plus:U21:U22:x -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c3 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
c4 :: c2:c3:c4
A__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c5:c6
c5 :: c7:c8:c9:c10 -> c5:c6
A__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c7:c8:c9:c10
c6 :: c5:c6
c7 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
a__x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
A__X :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c14:c15:c16
c8 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c9 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
0' :: tt:0':s:U11:U12:plus:U21:U22:x
c11 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c11:c12:c13
s :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c12 :: c:c1 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c14:c15:c16
c15 :: c5:c6 -> c14:c15:c16
c16 :: c14:c15:c16
U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c17 :: c:c1 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c18 :: c2:c3:c4 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c19 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c20 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c21 :: c5:c6 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c22 :: c7:c8:c9:c10 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c23 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c24 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c25 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c26 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c27 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
a__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
hole_c:c11_28 :: c:c1
hole_tt:0':s:U11:U12:plus:U21:U22:x2_28 :: tt:0':s:U11:U12:plus:U21:U22:x
hole_c2:c3:c43_28 :: c2:c3:c4
hole_c11:c12:c134_28 :: c11:c12:c13
hole_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c275_28 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
hole_c5:c66_28 :: c5:c6
hole_c7:c8:c9:c107_28 :: c7:c8:c9:c10
hole_c14:c15:c168_28 :: c14:c15:c16
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28 :: Nat -> tt:0':s:U11:U12:plus:U21:U22:x
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28 :: Nat -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27


Lemmas:
mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28)) -> gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28), rt in Omega(0)
a__U21(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n231132_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U22(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n253794_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n275862_28))) -> *11_28, rt in Omega(0)
a__U11(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n298923_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n309027_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__plus(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n212992_28))) -> *11_28, rt in Omega(0)


Generator Equations:
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0) <=> tt
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(x))
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(0) <=> c25
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(+(x, 1)) <=> c17(c(c2(c11(c25), c25)), gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(x))


The following defined symbols remain to be analysed:
A__U12, A__U11, A__PLUS, MARK, A__U21, A__U22, A__X

They will be analysed ascendingly in the following order:
A__U11 = A__U12
A__U11 = A__PLUS
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__U22
A__U11 = A__X
A__U12 = A__PLUS
A__U12 = MARK
A__U12 = A__U21
A__U12 = A__U22
A__U12 = A__X
A__PLUS = MARK
A__PLUS = A__U21
A__PLUS = A__U22
A__PLUS = A__X
MARK = A__U21
MARK = A__U22
MARK = A__X
A__U21 = A__U22
A__U21 = A__X
A__U22 = A__X

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

(41) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
A__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n318523_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(n318523_28)

Induction Base:
A__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))

Induction Step:
A__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(n318523_28, 1)), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) ->_R^Omega(1)
c2(A__PLUS(mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(n318523_28, 1)))), MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_L^Omega(0)
c2(A__PLUS(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n318523_28)))), MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_L^Omega(0)
c2(A__PLUS(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n318523_28))), MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_R^Omega(1)
c2(c12(A__U11(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n318523_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))), MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_R^Omega(1)
c2(c12(c(A__U12(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n318523_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)))), MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_IH
c2(c12(c(*11_28)), MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)))

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
----------------------------------------

(42)
Complex Obligation (BEST)

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

(43)
Obligation:
Proved the lower bound n^1 for the following obligation:

Innermost TRS:
Rules:
A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
A__U11(z0, z1, z2) -> c1
A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U12(z0, z1, z2) -> c4
A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
A__U21(z0, z1, z2) -> c6
A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U22(z0, z1, z2) -> c10
A__PLUS(z0, 0') -> c11(MARK(z0))
A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
A__PLUS(z0, z1) -> c13
A__X(z0, 0') -> c14
A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
A__X(z0, z1) -> c16
MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(tt) -> c25
MARK(s(z0)) -> c26(MARK(z0))
MARK(0') -> c27
a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
a__U11(z0, z1, z2) -> U11(z0, z1, z2)
a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U12(z0, z1, z2) -> U12(z0, z1, z2)
a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U22(z0, z1, z2) -> U22(z0, z1, z2)
a__plus(z0, 0') -> mark(z0)
a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> 0'
a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c:c1
tt :: tt:0':s:U11:U12:plus:U21:U22:x
c :: c2:c3:c4 -> c:c1
A__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c2:c3:c4
c1 :: c:c1
c2 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
A__PLUS :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c11:c12:c13
mark :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
MARK :: tt:0':s:U11:U12:plus:U21:U22:x -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c3 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
c4 :: c2:c3:c4
A__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c5:c6
c5 :: c7:c8:c9:c10 -> c5:c6
A__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c7:c8:c9:c10
c6 :: c5:c6
c7 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
a__x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
A__X :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c14:c15:c16
c8 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c9 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
0' :: tt:0':s:U11:U12:plus:U21:U22:x
c11 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c11:c12:c13
s :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c12 :: c:c1 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c14:c15:c16
c15 :: c5:c6 -> c14:c15:c16
c16 :: c14:c15:c16
U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c17 :: c:c1 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c18 :: c2:c3:c4 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c19 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c20 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c21 :: c5:c6 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c22 :: c7:c8:c9:c10 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c23 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c24 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c25 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c26 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c27 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
a__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
hole_c:c11_28 :: c:c1
hole_tt:0':s:U11:U12:plus:U21:U22:x2_28 :: tt:0':s:U11:U12:plus:U21:U22:x
hole_c2:c3:c43_28 :: c2:c3:c4
hole_c11:c12:c134_28 :: c11:c12:c13
hole_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c275_28 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
hole_c5:c66_28 :: c5:c6
hole_c7:c8:c9:c107_28 :: c7:c8:c9:c10
hole_c14:c15:c168_28 :: c14:c15:c16
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28 :: Nat -> tt:0':s:U11:U12:plus:U21:U22:x
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28 :: Nat -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27


Lemmas:
mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28)) -> gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28), rt in Omega(0)
a__U21(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n231132_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U22(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n253794_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n275862_28))) -> *11_28, rt in Omega(0)
a__U11(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n298923_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n309027_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__plus(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n212992_28))) -> *11_28, rt in Omega(0)


Generator Equations:
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0) <=> tt
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(x))
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(0) <=> c25
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(+(x, 1)) <=> c17(c(c2(c11(c25), c25)), gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(x))


The following defined symbols remain to be analysed:
A__U12, A__U11, A__PLUS, MARK, A__U21, A__U22, A__X

They will be analysed ascendingly in the following order:
A__U11 = A__U12
A__U11 = A__PLUS
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__U22
A__U11 = A__X
A__U12 = A__PLUS
A__U12 = MARK
A__U12 = A__U21
A__U12 = A__U22
A__U12 = A__X
A__PLUS = MARK
A__PLUS = A__U21
A__PLUS = A__U22
A__PLUS = A__X
MARK = A__U21
MARK = A__U22
MARK = A__X
A__U21 = A__U22
A__U21 = A__X
A__U22 = A__X

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

(44) LowerBoundPropagationProof (FINISHED)
Propagated lower bound.
----------------------------------------

(45)
BOUNDS(n^1, INF)

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

(46)
Obligation:
Innermost TRS:
Rules:
A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
A__U11(z0, z1, z2) -> c1
A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U12(z0, z1, z2) -> c4
A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
A__U21(z0, z1, z2) -> c6
A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U22(z0, z1, z2) -> c10
A__PLUS(z0, 0') -> c11(MARK(z0))
A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
A__PLUS(z0, z1) -> c13
A__X(z0, 0') -> c14
A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
A__X(z0, z1) -> c16
MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(tt) -> c25
MARK(s(z0)) -> c26(MARK(z0))
MARK(0') -> c27
a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
a__U11(z0, z1, z2) -> U11(z0, z1, z2)
a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U12(z0, z1, z2) -> U12(z0, z1, z2)
a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U22(z0, z1, z2) -> U22(z0, z1, z2)
a__plus(z0, 0') -> mark(z0)
a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> 0'
a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c:c1
tt :: tt:0':s:U11:U12:plus:U21:U22:x
c :: c2:c3:c4 -> c:c1
A__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c2:c3:c4
c1 :: c:c1
c2 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
A__PLUS :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c11:c12:c13
mark :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
MARK :: tt:0':s:U11:U12:plus:U21:U22:x -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c3 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
c4 :: c2:c3:c4
A__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c5:c6
c5 :: c7:c8:c9:c10 -> c5:c6
A__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c7:c8:c9:c10
c6 :: c5:c6
c7 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
a__x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
A__X :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c14:c15:c16
c8 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c9 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
0' :: tt:0':s:U11:U12:plus:U21:U22:x
c11 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c11:c12:c13
s :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c12 :: c:c1 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c14:c15:c16
c15 :: c5:c6 -> c14:c15:c16
c16 :: c14:c15:c16
U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c17 :: c:c1 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c18 :: c2:c3:c4 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c19 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c20 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c21 :: c5:c6 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c22 :: c7:c8:c9:c10 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c23 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c24 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c25 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c26 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c27 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
a__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
hole_c:c11_28 :: c:c1
hole_tt:0':s:U11:U12:plus:U21:U22:x2_28 :: tt:0':s:U11:U12:plus:U21:U22:x
hole_c2:c3:c43_28 :: c2:c3:c4
hole_c11:c12:c134_28 :: c11:c12:c13
hole_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c275_28 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
hole_c5:c66_28 :: c5:c6
hole_c7:c8:c9:c107_28 :: c7:c8:c9:c10
hole_c14:c15:c168_28 :: c14:c15:c16
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28 :: Nat -> tt:0':s:U11:U12:plus:U21:U22:x
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28 :: Nat -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27


Lemmas:
mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28)) -> gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28), rt in Omega(0)
a__U21(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n231132_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U22(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n253794_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n275862_28))) -> *11_28, rt in Omega(0)
a__U11(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n298923_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n309027_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__plus(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n212992_28))) -> *11_28, rt in Omega(0)
A__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n318523_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(n318523_28)


Generator Equations:
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0) <=> tt
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(x))
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(0) <=> c25
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(+(x, 1)) <=> c17(c(c2(c11(c25), c25)), gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(x))


The following defined symbols remain to be analysed:
A__PLUS, A__U11, MARK, A__U21, A__U22, A__X

They will be analysed ascendingly in the following order:
A__U11 = A__U12
A__U11 = A__PLUS
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__U22
A__U11 = A__X
A__U12 = A__PLUS
A__U12 = MARK
A__U12 = A__U21
A__U12 = A__U22
A__U12 = A__X
A__PLUS = MARK
A__PLUS = A__U21
A__PLUS = A__U22
A__PLUS = A__X
MARK = A__U21
MARK = A__U22
MARK = A__X
A__U21 = A__U22
A__U21 = A__X
A__U22 = A__X

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

(47) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
A__PLUS(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n337199_28))) -> *11_28, rt in Omega(n337199_28)

Induction Base:
A__PLUS(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, 0)))

Induction Step:
A__PLUS(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, +(n337199_28, 1)))) ->_R^Omega(1)
c12(A__U11(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n337199_28)), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a))) ->_R^Omega(1)
c12(c(A__U12(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n337199_28)), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a)))) ->_R^Omega(1)
c12(c(c2(A__PLUS(mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a)), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n337199_28)))), MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a))))) ->_L^Omega(0)
c12(c(c2(A__PLUS(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n337199_28)))), MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a))))) ->_L^Omega(0)
c12(c(c2(A__PLUS(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n337199_28))), MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a))))) ->_IH
c12(c(c2(*11_28, MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a)))))

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
----------------------------------------

(48)
Obligation:
Innermost TRS:
Rules:
A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
A__U11(z0, z1, z2) -> c1
A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U12(z0, z1, z2) -> c4
A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
A__U21(z0, z1, z2) -> c6
A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U22(z0, z1, z2) -> c10
A__PLUS(z0, 0') -> c11(MARK(z0))
A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
A__PLUS(z0, z1) -> c13
A__X(z0, 0') -> c14
A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
A__X(z0, z1) -> c16
MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(tt) -> c25
MARK(s(z0)) -> c26(MARK(z0))
MARK(0') -> c27
a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
a__U11(z0, z1, z2) -> U11(z0, z1, z2)
a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U12(z0, z1, z2) -> U12(z0, z1, z2)
a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U22(z0, z1, z2) -> U22(z0, z1, z2)
a__plus(z0, 0') -> mark(z0)
a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> 0'
a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c:c1
tt :: tt:0':s:U11:U12:plus:U21:U22:x
c :: c2:c3:c4 -> c:c1
A__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c2:c3:c4
c1 :: c:c1
c2 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
A__PLUS :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c11:c12:c13
mark :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
MARK :: tt:0':s:U11:U12:plus:U21:U22:x -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c3 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
c4 :: c2:c3:c4
A__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c5:c6
c5 :: c7:c8:c9:c10 -> c5:c6
A__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c7:c8:c9:c10
c6 :: c5:c6
c7 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
a__x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
A__X :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c14:c15:c16
c8 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c9 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
0' :: tt:0':s:U11:U12:plus:U21:U22:x
c11 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c11:c12:c13
s :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c12 :: c:c1 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c14:c15:c16
c15 :: c5:c6 -> c14:c15:c16
c16 :: c14:c15:c16
U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c17 :: c:c1 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c18 :: c2:c3:c4 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c19 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c20 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c21 :: c5:c6 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c22 :: c7:c8:c9:c10 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c23 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c24 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c25 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c26 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c27 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
a__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
hole_c:c11_28 :: c:c1
hole_tt:0':s:U11:U12:plus:U21:U22:x2_28 :: tt:0':s:U11:U12:plus:U21:U22:x
hole_c2:c3:c43_28 :: c2:c3:c4
hole_c11:c12:c134_28 :: c11:c12:c13
hole_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c275_28 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
hole_c5:c66_28 :: c5:c6
hole_c7:c8:c9:c107_28 :: c7:c8:c9:c10
hole_c14:c15:c168_28 :: c14:c15:c16
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28 :: Nat -> tt:0':s:U11:U12:plus:U21:U22:x
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28 :: Nat -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27


Lemmas:
mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28)) -> gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28), rt in Omega(0)
a__U21(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n231132_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U22(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n253794_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n275862_28))) -> *11_28, rt in Omega(0)
a__U11(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n298923_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n309027_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__plus(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n212992_28))) -> *11_28, rt in Omega(0)
A__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n318523_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(n318523_28)
A__PLUS(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n337199_28))) -> *11_28, rt in Omega(n337199_28)


Generator Equations:
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0) <=> tt
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(x))
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(0) <=> c25
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(+(x, 1)) <=> c17(c(c2(c11(c25), c25)), gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(x))


The following defined symbols remain to be analysed:
MARK, A__U11, A__U12, A__U21, A__U22, A__X

They will be analysed ascendingly in the following order:
A__U11 = A__U12
A__U11 = A__PLUS
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__U22
A__U11 = A__X
A__U12 = A__PLUS
A__U12 = MARK
A__U12 = A__U21
A__U12 = A__U22
A__U12 = A__X
A__PLUS = MARK
A__PLUS = A__U21
A__PLUS = A__U22
A__PLUS = A__X
MARK = A__U21
MARK = A__U22
MARK = A__X
A__U21 = A__U22
A__U21 = A__X
A__U22 = A__X

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

(49) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n356929_28))) -> *11_28, rt in Omega(n356929_28)

Induction Base:
MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, 0)))

Induction Step:
MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, +(n356929_28, 1)))) ->_R^Omega(1)
c26(MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n356929_28)))) ->_IH
c26(*11_28)

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
----------------------------------------

(50)
Obligation:
Innermost TRS:
Rules:
A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
A__U11(z0, z1, z2) -> c1
A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U12(z0, z1, z2) -> c4
A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
A__U21(z0, z1, z2) -> c6
A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U22(z0, z1, z2) -> c10
A__PLUS(z0, 0') -> c11(MARK(z0))
A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
A__PLUS(z0, z1) -> c13
A__X(z0, 0') -> c14
A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
A__X(z0, z1) -> c16
MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(tt) -> c25
MARK(s(z0)) -> c26(MARK(z0))
MARK(0') -> c27
a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
a__U11(z0, z1, z2) -> U11(z0, z1, z2)
a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U12(z0, z1, z2) -> U12(z0, z1, z2)
a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U22(z0, z1, z2) -> U22(z0, z1, z2)
a__plus(z0, 0') -> mark(z0)
a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> 0'
a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c:c1
tt :: tt:0':s:U11:U12:plus:U21:U22:x
c :: c2:c3:c4 -> c:c1
A__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c2:c3:c4
c1 :: c:c1
c2 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
A__PLUS :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c11:c12:c13
mark :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
MARK :: tt:0':s:U11:U12:plus:U21:U22:x -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c3 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
c4 :: c2:c3:c4
A__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c5:c6
c5 :: c7:c8:c9:c10 -> c5:c6
A__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c7:c8:c9:c10
c6 :: c5:c6
c7 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
a__x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
A__X :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c14:c15:c16
c8 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c9 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
0' :: tt:0':s:U11:U12:plus:U21:U22:x
c11 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c11:c12:c13
s :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c12 :: c:c1 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c14:c15:c16
c15 :: c5:c6 -> c14:c15:c16
c16 :: c14:c15:c16
U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c17 :: c:c1 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c18 :: c2:c3:c4 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c19 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c20 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c21 :: c5:c6 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c22 :: c7:c8:c9:c10 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c23 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c24 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c25 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c26 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c27 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
a__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
hole_c:c11_28 :: c:c1
hole_tt:0':s:U11:U12:plus:U21:U22:x2_28 :: tt:0':s:U11:U12:plus:U21:U22:x
hole_c2:c3:c43_28 :: c2:c3:c4
hole_c11:c12:c134_28 :: c11:c12:c13
hole_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c275_28 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
hole_c5:c66_28 :: c5:c6
hole_c7:c8:c9:c107_28 :: c7:c8:c9:c10
hole_c14:c15:c168_28 :: c14:c15:c16
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28 :: Nat -> tt:0':s:U11:U12:plus:U21:U22:x
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28 :: Nat -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27


Lemmas:
mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28)) -> gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28), rt in Omega(0)
a__U21(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n231132_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U22(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n253794_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n275862_28))) -> *11_28, rt in Omega(0)
a__U11(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n298923_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n309027_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__plus(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n212992_28))) -> *11_28, rt in Omega(0)
A__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n318523_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(n318523_28)
A__PLUS(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n337199_28))) -> *11_28, rt in Omega(n337199_28)
MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n356929_28))) -> *11_28, rt in Omega(n356929_28)


Generator Equations:
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0) <=> tt
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(x))
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(0) <=> c25
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(+(x, 1)) <=> c17(c(c2(c11(c25), c25)), gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(x))


The following defined symbols remain to be analysed:
A__U11, A__U12, A__PLUS, A__U21, A__U22, A__X

They will be analysed ascendingly in the following order:
A__U11 = A__U12
A__U11 = A__PLUS
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__U22
A__U11 = A__X
A__U12 = A__PLUS
A__U12 = MARK
A__U12 = A__U21
A__U12 = A__U22
A__U12 = A__X
A__PLUS = MARK
A__PLUS = A__U21
A__PLUS = A__U22
A__PLUS = A__X
MARK = A__U21
MARK = A__U22
MARK = A__X
A__U21 = A__U22
A__U21 = A__X
A__U22 = A__X

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

(51) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
A__U11(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n488416_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(n488416_28)

Induction Base:
A__U11(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))

Induction Step:
A__U11(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(n488416_28, 1)), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) ->_R^Omega(1)
c(A__U12(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(n488416_28, 1)), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_R^Omega(1)
c(c2(A__PLUS(mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n488416_28)))), MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)))) ->_L^Omega(0)
c(c2(A__PLUS(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n488416_28)))), MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)))) ->_L^Omega(0)
c(c2(A__PLUS(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n488416_28))), MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)))) ->_R^Omega(1)
c(c2(c12(A__U11(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n488416_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))), MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)))) ->_IH
c(c2(c12(*11_28), MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))))

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
----------------------------------------

(52)
Obligation:
Innermost TRS:
Rules:
A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
A__U11(z0, z1, z2) -> c1
A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U12(z0, z1, z2) -> c4
A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
A__U21(z0, z1, z2) -> c6
A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U22(z0, z1, z2) -> c10
A__PLUS(z0, 0') -> c11(MARK(z0))
A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
A__PLUS(z0, z1) -> c13
A__X(z0, 0') -> c14
A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
A__X(z0, z1) -> c16
MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(tt) -> c25
MARK(s(z0)) -> c26(MARK(z0))
MARK(0') -> c27
a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
a__U11(z0, z1, z2) -> U11(z0, z1, z2)
a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U12(z0, z1, z2) -> U12(z0, z1, z2)
a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U22(z0, z1, z2) -> U22(z0, z1, z2)
a__plus(z0, 0') -> mark(z0)
a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> 0'
a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c:c1
tt :: tt:0':s:U11:U12:plus:U21:U22:x
c :: c2:c3:c4 -> c:c1
A__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c2:c3:c4
c1 :: c:c1
c2 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
A__PLUS :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c11:c12:c13
mark :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
MARK :: tt:0':s:U11:U12:plus:U21:U22:x -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c3 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
c4 :: c2:c3:c4
A__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c5:c6
c5 :: c7:c8:c9:c10 -> c5:c6
A__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c7:c8:c9:c10
c6 :: c5:c6
c7 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
a__x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
A__X :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c14:c15:c16
c8 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c9 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
0' :: tt:0':s:U11:U12:plus:U21:U22:x
c11 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c11:c12:c13
s :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c12 :: c:c1 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c14:c15:c16
c15 :: c5:c6 -> c14:c15:c16
c16 :: c14:c15:c16
U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c17 :: c:c1 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c18 :: c2:c3:c4 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c19 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c20 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c21 :: c5:c6 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c22 :: c7:c8:c9:c10 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c23 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c24 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c25 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c26 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c27 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
a__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
hole_c:c11_28 :: c:c1
hole_tt:0':s:U11:U12:plus:U21:U22:x2_28 :: tt:0':s:U11:U12:plus:U21:U22:x
hole_c2:c3:c43_28 :: c2:c3:c4
hole_c11:c12:c134_28 :: c11:c12:c13
hole_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c275_28 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
hole_c5:c66_28 :: c5:c6
hole_c7:c8:c9:c107_28 :: c7:c8:c9:c10
hole_c14:c15:c168_28 :: c14:c15:c16
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28 :: Nat -> tt:0':s:U11:U12:plus:U21:U22:x
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28 :: Nat -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27


Lemmas:
mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28)) -> gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28), rt in Omega(0)
a__U21(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n231132_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U22(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n253794_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n275862_28))) -> *11_28, rt in Omega(0)
a__U11(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n298923_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n309027_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__plus(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n212992_28))) -> *11_28, rt in Omega(0)
A__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n318523_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(n318523_28)
A__PLUS(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n337199_28))) -> *11_28, rt in Omega(n337199_28)
MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n356929_28))) -> *11_28, rt in Omega(n356929_28)
A__U11(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n488416_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(n488416_28)


Generator Equations:
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0) <=> tt
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(x))
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(0) <=> c25
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(+(x, 1)) <=> c17(c(c2(c11(c25), c25)), gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(x))


The following defined symbols remain to be analysed:
A__U21, A__U12, A__PLUS, MARK, A__U22, A__X

They will be analysed ascendingly in the following order:
A__U11 = A__U12
A__U11 = A__PLUS
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__U22
A__U11 = A__X
A__U12 = A__PLUS
A__U12 = MARK
A__U12 = A__U21
A__U12 = A__U22
A__U12 = A__X
A__PLUS = MARK
A__PLUS = A__U21
A__PLUS = A__U22
A__PLUS = A__X
MARK = A__U21
MARK = A__U22
MARK = A__X
A__U21 = A__U22
A__U21 = A__X
A__U22 = A__X

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

(53) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
A__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n518699_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(n518699_28)

Induction Base:
A__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))

Induction Step:
A__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(n518699_28, 1)), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) ->_R^Omega(1)
c2(A__PLUS(mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(n518699_28, 1)))), MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_L^Omega(0)
c2(A__PLUS(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n518699_28)))), MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_L^Omega(0)
c2(A__PLUS(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n518699_28))), MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_R^Omega(1)
c2(c12(A__U11(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n518699_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))), MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_R^Omega(1)
c2(c12(c(A__U12(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n518699_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)))), MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c))) ->_IH
c2(c12(c(*11_28)), MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)))

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
----------------------------------------

(54)
Obligation:
Innermost TRS:
Rules:
A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
A__U11(z0, z1, z2) -> c1
A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U12(z0, z1, z2) -> c4
A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
A__U21(z0, z1, z2) -> c6
A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U22(z0, z1, z2) -> c10
A__PLUS(z0, 0') -> c11(MARK(z0))
A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
A__PLUS(z0, z1) -> c13
A__X(z0, 0') -> c14
A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
A__X(z0, z1) -> c16
MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(tt) -> c25
MARK(s(z0)) -> c26(MARK(z0))
MARK(0') -> c27
a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
a__U11(z0, z1, z2) -> U11(z0, z1, z2)
a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U12(z0, z1, z2) -> U12(z0, z1, z2)
a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U22(z0, z1, z2) -> U22(z0, z1, z2)
a__plus(z0, 0') -> mark(z0)
a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> 0'
a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c:c1
tt :: tt:0':s:U11:U12:plus:U21:U22:x
c :: c2:c3:c4 -> c:c1
A__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c2:c3:c4
c1 :: c:c1
c2 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
A__PLUS :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c11:c12:c13
mark :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
MARK :: tt:0':s:U11:U12:plus:U21:U22:x -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c3 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
c4 :: c2:c3:c4
A__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c5:c6
c5 :: c7:c8:c9:c10 -> c5:c6
A__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c7:c8:c9:c10
c6 :: c5:c6
c7 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
a__x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
A__X :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c14:c15:c16
c8 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c9 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
0' :: tt:0':s:U11:U12:plus:U21:U22:x
c11 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c11:c12:c13
s :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c12 :: c:c1 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c14:c15:c16
c15 :: c5:c6 -> c14:c15:c16
c16 :: c14:c15:c16
U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c17 :: c:c1 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c18 :: c2:c3:c4 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c19 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c20 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c21 :: c5:c6 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c22 :: c7:c8:c9:c10 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c23 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c24 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c25 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c26 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c27 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
a__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
hole_c:c11_28 :: c:c1
hole_tt:0':s:U11:U12:plus:U21:U22:x2_28 :: tt:0':s:U11:U12:plus:U21:U22:x
hole_c2:c3:c43_28 :: c2:c3:c4
hole_c11:c12:c134_28 :: c11:c12:c13
hole_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c275_28 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
hole_c5:c66_28 :: c5:c6
hole_c7:c8:c9:c107_28 :: c7:c8:c9:c10
hole_c14:c15:c168_28 :: c14:c15:c16
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28 :: Nat -> tt:0':s:U11:U12:plus:U21:U22:x
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28 :: Nat -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27


Lemmas:
mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28)) -> gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28), rt in Omega(0)
a__U21(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n231132_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U22(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n253794_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n275862_28))) -> *11_28, rt in Omega(0)
a__U11(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n298923_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n309027_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__plus(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n212992_28))) -> *11_28, rt in Omega(0)
A__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n518699_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(n518699_28)
A__PLUS(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n337199_28))) -> *11_28, rt in Omega(n337199_28)
MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n356929_28))) -> *11_28, rt in Omega(n356929_28)
A__U11(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n488416_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(n488416_28)


Generator Equations:
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0) <=> tt
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(x))
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(0) <=> c25
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(+(x, 1)) <=> c17(c(c2(c11(c25), c25)), gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(x))


The following defined symbols remain to be analysed:
A__PLUS, MARK

They will be analysed ascendingly in the following order:
A__U11 = A__U12
A__U11 = A__PLUS
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__U22
A__U11 = A__X
A__U12 = A__PLUS
A__U12 = MARK
A__U12 = A__U21
A__U12 = A__U22
A__U12 = A__X
A__PLUS = MARK
A__PLUS = A__U21
A__PLUS = A__U22
A__PLUS = A__X
MARK = A__U21
MARK = A__U22
MARK = A__X
A__U21 = A__U22
A__U21 = A__X
A__U22 = A__X

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

(55) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
A__PLUS(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n539232_28))) -> *11_28, rt in Omega(n539232_28)

Induction Base:
A__PLUS(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, 0)))

Induction Step:
A__PLUS(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, +(n539232_28, 1)))) ->_R^Omega(1)
c12(A__U11(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n539232_28)), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a))) ->_R^Omega(1)
c12(c(A__U12(tt, gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n539232_28)), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a)))) ->_R^Omega(1)
c12(c(c2(A__PLUS(mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a)), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n539232_28)))), MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a))))) ->_L^Omega(0)
c12(c(c2(A__PLUS(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n539232_28)))), MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a))))) ->_L^Omega(0)
c12(c(c2(A__PLUS(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n539232_28))), MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a))))) ->_IH
c12(c(c2(*11_28, MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a)))))

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
----------------------------------------

(56)
Obligation:
Innermost TRS:
Rules:
A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
A__U11(z0, z1, z2) -> c1
A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U12(z0, z1, z2) -> c4
A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
A__U21(z0, z1, z2) -> c6
A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
A__U22(z0, z1, z2) -> c10
A__PLUS(z0, 0') -> c11(MARK(z0))
A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
A__PLUS(z0, z1) -> c13
A__X(z0, 0') -> c14
A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
A__X(z0, z1) -> c16
MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
MARK(tt) -> c25
MARK(s(z0)) -> c26(MARK(z0))
MARK(0') -> c27
a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
a__U11(z0, z1, z2) -> U11(z0, z1, z2)
a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U12(z0, z1, z2) -> U12(z0, z1, z2)
a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
a__U21(z0, z1, z2) -> U21(z0, z1, z2)
a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
a__U22(z0, z1, z2) -> U22(z0, z1, z2)
a__plus(z0, 0') -> mark(z0)
a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
a__x(z0, 0') -> 0'
a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
a__x(z0, z1) -> x(z0, z1)
mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c:c1
tt :: tt:0':s:U11:U12:plus:U21:U22:x
c :: c2:c3:c4 -> c:c1
A__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c2:c3:c4
c1 :: c:c1
c2 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
A__PLUS :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c11:c12:c13
mark :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
MARK :: tt:0':s:U11:U12:plus:U21:U22:x -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c3 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c2:c3:c4
c4 :: c2:c3:c4
A__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c5:c6
c5 :: c7:c8:c9:c10 -> c5:c6
A__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c7:c8:c9:c10
c6 :: c5:c6
c7 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
a__x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
A__X :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> c14:c15:c16
c8 :: c11:c12:c13 -> c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c9 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c7:c8:c9:c10
c10 :: c7:c8:c9:c10
0' :: tt:0':s:U11:U12:plus:U21:U22:x
c11 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c11:c12:c13
s :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c12 :: c:c1 -> c11:c12:c13
c13 :: c11:c12:c13
c14 :: c14:c15:c16
c15 :: c5:c6 -> c14:c15:c16
c16 :: c14:c15:c16
U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c17 :: c:c1 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c18 :: c2:c3:c4 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c19 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c20 :: c11:c12:c13 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c21 :: c5:c6 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c22 :: c7:c8:c9:c10 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
x :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
c23 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c24 :: c14:c15:c16 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c25 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c26 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27 -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
c27 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
a__U11 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U12 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__plus :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U21 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
a__U22 :: tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x -> tt:0':s:U11:U12:plus:U21:U22:x
hole_c:c11_28 :: c:c1
hole_tt:0':s:U11:U12:plus:U21:U22:x2_28 :: tt:0':s:U11:U12:plus:U21:U22:x
hole_c2:c3:c43_28 :: c2:c3:c4
hole_c11:c12:c134_28 :: c11:c12:c13
hole_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c275_28 :: c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27
hole_c5:c66_28 :: c5:c6
hole_c7:c8:c9:c107_28 :: c7:c8:c9:c10
hole_c14:c15:c168_28 :: c14:c15:c16
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28 :: Nat -> tt:0':s:U11:U12:plus:U21:U22:x
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28 :: Nat -> c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27


Lemmas:
mark(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28)) -> gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n223086_28), rt in Omega(0)
a__U21(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n231132_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U22(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n253794_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__x(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n275862_28))) -> *11_28, rt in Omega(0)
a__U11(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n298923_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n309027_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(0)
a__plus(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n212992_28))) -> *11_28, rt in Omega(0)
A__U12(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n518699_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(n518699_28)
A__PLUS(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(a), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n539232_28))) -> *11_28, rt in Omega(n539232_28)
MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n356929_28))) -> *11_28, rt in Omega(n356929_28)
A__U11(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(n488416_28), gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(c)) -> *11_28, rt in Omega(n488416_28)


Generator Equations:
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(0) <=> tt
gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(x, 1)) <=> s(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(x))
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(0) <=> c25
gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(+(x, 1)) <=> c17(c(c2(c11(c25), c25)), gen_c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c2710_28(x))


The following defined symbols remain to be analysed:
MARK

They will be analysed ascendingly in the following order:
A__U11 = A__U12
A__U11 = A__PLUS
A__U11 = MARK
A__U11 = A__U21
A__U11 = A__U22
A__U11 = A__X
A__U12 = A__PLUS
A__U12 = MARK
A__U12 = A__U21
A__U12 = A__U22
A__U12 = A__X
A__PLUS = MARK
A__PLUS = A__U21
A__PLUS = A__U22
A__PLUS = A__X
MARK = A__U21
MARK = A__U22
MARK = A__X
A__U21 = A__U22
A__U21 = A__X
A__U22 = A__X

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

(57) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n560345_28))) -> *11_28, rt in Omega(n560345_28)

Induction Base:
MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, 0)))

Induction Step:
MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, +(n560345_28, 1)))) ->_R^Omega(1)
c26(MARK(gen_tt:0':s:U11:U12:plus:U21:U22:x9_28(+(1, n560345_28)))) ->_IH
c26(*11_28)

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
----------------------------------------

(58)
BOUNDS(1, INF)

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

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

(60)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U11(z0, z1, z2) -> c1
   A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U12(z0, z1, z2) -> c4
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__U21(z0, z1, z2) -> c6
   A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__U22(z0, z1, z2) -> c10
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__PLUS(z0, z1) -> c13
   A__X(z0, 0) -> c14
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   A__X(z0, z1) -> c16
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(tt) -> c25
   MARK(s(z0)) -> c26(MARK(z0))
   MARK(0) -> c27
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U11(z0, z1, z2) -> c1
   A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U12(z0, z1, z2) -> c4
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__U21(z0, z1, z2) -> c6
   A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__U22(z0, z1, z2) -> c10
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__PLUS(z0, z1) -> c13
   A__X(z0, 0) -> c14
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   A__X(z0, z1) -> c16
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(tt) -> c25
   MARK(s(z0)) -> c26(MARK(z0))
   MARK(0) -> c27
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U12_3, A__U21_3, A__U22_3, A__PLUS_2, A__X_2, MARK_1

Compound Symbols:   c_1, c1, c2_2, c3_2, c4, c5_1, c6, c7_3, c8_3, c9_2, c10, c11_1, c12_1, c13, c14, c15_1, c16, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c25, c26_1, c27


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

(61) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 9 trailing nodes:
   A__U21(z0, z1, z2) -> c6
   A__U11(z0, z1, z2) -> c1
   MARK(tt) -> c25
   A__U22(z0, z1, z2) -> c10
   MARK(0) -> c27
   A__X(z0, 0) -> c14
   A__PLUS(z0, z1) -> c13
   A__U12(z0, z1, z2) -> c4
   A__X(z0, z1) -> c16

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

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U12_3, A__U21_3, A__U22_3, A__PLUS_2, A__X_2, MARK_1

Compound Symbols:   c_1, c2_2, c3_2, c5_1, c7_3, c8_3, c9_2, c11_1, c12_1, c15_1, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c26_1


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

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

(64)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))

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

   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0

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

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

(66)
Obligation:
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0

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

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

(68)
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, z0, z1) -> c(A__U12(tt, z0, z1)) [1]
   A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1]
   A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1]
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1)) [1]
   A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) [1]
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) [1]
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) [1]
   A__PLUS(z0, 0) -> c11(MARK(z0)) [1]
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0)) [1]
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0)) [1]
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(s(z0)) -> c26(MARK(z0)) [1]
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) [0]
   a__U11(z0, z1, z2) -> U11(z0, z1, z2) [0]
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0]
   a__U12(z0, z1, z2) -> U12(z0, z1, z2) [0]
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1) [0]
   a__U21(z0, z1, z2) -> U21(z0, z1, z2) [0]
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) [0]
   a__U22(z0, z1, z2) -> U22(z0, z1, z2) [0]
   a__plus(z0, 0) -> mark(z0) [0]
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) [0]
   a__plus(z0, z1) -> plus(z0, z1) [0]
   a__x(z0, 0) -> 0 [0]
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0) [0]
   a__x(z0, z1) -> x(z0, z1) [0]
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) [0]
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) [0]
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0]
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) [0]
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2) [0]
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) [0]
   mark(tt) -> tt [0]
   mark(s(z0)) -> s(mark(z0)) [0]
   mark(0) -> 0 [0]

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

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

(70)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1)) [1]
   A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1]
   A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1]
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1)) [1]
   A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) [1]
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) [1]
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) [1]
   A__PLUS(z0, 0) -> c11(MARK(z0)) [1]
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0)) [1]
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0)) [1]
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(s(z0)) -> c26(MARK(z0)) [1]
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) [0]
   a__U11(z0, z1, z2) -> U11(z0, z1, z2) [0]
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0]
   a__U12(z0, z1, z2) -> U12(z0, z1, z2) [0]
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1) [0]
   a__U21(z0, z1, z2) -> U21(z0, z1, z2) [0]
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) [0]
   a__U22(z0, z1, z2) -> U22(z0, z1, z2) [0]
   a__plus(z0, 0) -> mark(z0) [0]
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) [0]
   a__plus(z0, z1) -> plus(z0, z1) [0]
   a__x(z0, 0) -> 0 [0]
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0) [0]
   a__x(z0, z1) -> x(z0, z1) [0]
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) [0]
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) [0]
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0]
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) [0]
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2) [0]
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) [0]
   mark(tt) -> tt [0]
   mark(s(z0)) -> s(mark(z0)) [0]
   mark(0) -> 0 [0]

The TRS has the following type information:
A__U11 :: tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> c
tt :: tt:0:s:U11:U12:plus:U21:U22:x
c :: c2:c3 -> c
A__U12 :: tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> c2:c3
c2 :: c11:c12 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c2:c3
A__PLUS :: tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> c11:c12
mark :: tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x
MARK :: tt:0:s:U11:U12:plus:U21:U22:x -> c17:c18:c19:c20:c21:c22:c23:c24:c26
c3 :: c11:c12 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c2:c3
A__U21 :: tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> c5
c5 :: c7:c8:c9 -> c5
A__U22 :: tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> c7:c8:c9
c7 :: c11:c12 -> c15 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c7:c8:c9
a__x :: tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x
A__X :: tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> c15
c8 :: c11:c12 -> c15 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c7:c8:c9
c9 :: c11:c12 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c7:c8:c9
0 :: tt:0:s:U11:U12:plus:U21:U22:x
c11 :: c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c11:c12
s :: tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x
c12 :: c -> c11:c12
c15 :: c5 -> c15
U11 :: tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x
c17 :: c -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c17:c18:c19:c20:c21:c22:c23:c24:c26
U12 :: tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x
c18 :: c2:c3 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c17:c18:c19:c20:c21:c22:c23:c24:c26
plus :: tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x
c19 :: c11:c12 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c17:c18:c19:c20:c21:c22:c23:c24:c26
c20 :: c11:c12 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c17:c18:c19:c20:c21:c22:c23:c24:c26
U21 :: tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x
c21 :: c5 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c17:c18:c19:c20:c21:c22:c23:c24:c26
U22 :: tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x
c22 :: c7:c8:c9 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c17:c18:c19:c20:c21:c22:c23:c24:c26
x :: tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x
c23 :: c15 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c17:c18:c19:c20:c21:c22:c23:c24:c26
c24 :: c15 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c17:c18:c19:c20:c21:c22:c23:c24:c26
c26 :: c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c17:c18:c19:c20:c21:c22:c23:c24:c26
a__U11 :: tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x
a__U12 :: tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x
a__plus :: tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x
a__U21 :: tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x
a__U22 :: tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x -> tt:0:s:U11:U12:plus:U21:U22:x

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

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

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

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

   A__U11_3
   A__U12_3
   A__U21_3
   A__U22_3
   A__PLUS_2
   A__X_2
   MARK_1

(c) The following functions are completely defined:

   a__U11_3
   a__U12_3
   a__U21_3
   a__U22_3
   a__plus_2
   a__x_2
   mark_1

Due to the following rules being added:

   a__U11(v0, v1, v2) -> null_a__U11 [0]
   a__U12(v0, v1, v2) -> null_a__U12 [0]
   a__U21(v0, v1, v2) -> null_a__U21 [0]
   a__U22(v0, v1, v2) -> null_a__U22 [0]
   a__plus(v0, v1) -> null_a__plus [0]
   a__x(v0, v1) -> null_a__x [0]
   mark(v0) -> null_mark [0]

And the following fresh constants:    null_a__U11, null_a__U12, null_a__U21, null_a__U22, null_a__plus, null_a__x, null_mark, const, const1, const2, const3, const4, const5, const6

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

(72)
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, z0, z1) -> c(A__U12(tt, z0, z1)) [1]
   A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1]
   A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1]
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1)) [1]
   A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) [1]
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) [1]
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) [1]
   A__PLUS(z0, 0) -> c11(MARK(z0)) [1]
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0)) [1]
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0)) [1]
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(s(z0)) -> c26(MARK(z0)) [1]
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) [0]
   a__U11(z0, z1, z2) -> U11(z0, z1, z2) [0]
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0]
   a__U12(z0, z1, z2) -> U12(z0, z1, z2) [0]
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1) [0]
   a__U21(z0, z1, z2) -> U21(z0, z1, z2) [0]
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) [0]
   a__U22(z0, z1, z2) -> U22(z0, z1, z2) [0]
   a__plus(z0, 0) -> mark(z0) [0]
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) [0]
   a__plus(z0, z1) -> plus(z0, z1) [0]
   a__x(z0, 0) -> 0 [0]
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0) [0]
   a__x(z0, z1) -> x(z0, z1) [0]
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) [0]
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) [0]
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0]
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) [0]
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2) [0]
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) [0]
   mark(tt) -> tt [0]
   mark(s(z0)) -> s(mark(z0)) [0]
   mark(0) -> 0 [0]
   a__U11(v0, v1, v2) -> null_a__U11 [0]
   a__U12(v0, v1, v2) -> null_a__U12 [0]
   a__U21(v0, v1, v2) -> null_a__U21 [0]
   a__U22(v0, v1, v2) -> null_a__U22 [0]
   a__plus(v0, v1) -> null_a__plus [0]
   a__x(v0, v1) -> null_a__x [0]
   mark(v0) -> null_mark [0]

The TRS has the following type information:
A__U11 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> c
tt :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
c :: c2:c3 -> c
A__U12 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> c2:c3
c2 :: c11:c12 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c2:c3
A__PLUS :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> c11:c12
mark :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
MARK :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> c17:c18:c19:c20:c21:c22:c23:c24:c26
c3 :: c11:c12 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c2:c3
A__U21 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> c5
c5 :: c7:c8:c9 -> c5
A__U22 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> c7:c8:c9
c7 :: c11:c12 -> c15 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c7:c8:c9
a__x :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
A__X :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> c15
c8 :: c11:c12 -> c15 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c7:c8:c9
c9 :: c11:c12 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c7:c8:c9
0 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
c11 :: c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c11:c12
s :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
c12 :: c -> c11:c12
c15 :: c5 -> c15
U11 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
c17 :: c -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c17:c18:c19:c20:c21:c22:c23:c24:c26
U12 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
c18 :: c2:c3 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c17:c18:c19:c20:c21:c22:c23:c24:c26
plus :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
c19 :: c11:c12 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c17:c18:c19:c20:c21:c22:c23:c24:c26
c20 :: c11:c12 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c17:c18:c19:c20:c21:c22:c23:c24:c26
U21 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
c21 :: c5 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c17:c18:c19:c20:c21:c22:c23:c24:c26
U22 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
c22 :: c7:c8:c9 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c17:c18:c19:c20:c21:c22:c23:c24:c26
x :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
c23 :: c15 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c17:c18:c19:c20:c21:c22:c23:c24:c26
c24 :: c15 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c17:c18:c19:c20:c21:c22:c23:c24:c26
c26 :: c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c17:c18:c19:c20:c21:c22:c23:c24:c26
a__U11 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
a__U12 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
a__plus :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
a__U21 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
a__U22 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
null_a__U11 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
null_a__U12 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
null_a__U21 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
null_a__U22 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
null_a__plus :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
null_a__x :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
null_mark :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
const :: c
const1 :: c2:c3
const2 :: c11:c12
const3 :: c17:c18:c19:c20:c21:c22:c23:c24:c26
const4 :: c5
const5 :: c7:c8:c9
const6 :: c15

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

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

(74)
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, z0, z1) -> c(A__U12(tt, z0, z1)) [1]
   A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1]
   A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1]
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1)) [1]
   A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) [1]
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) [1]
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) [1]
   A__PLUS(z0, 0) -> c11(MARK(z0)) [1]
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0)) [1]
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0)) [1]
   MARK(U11(U11(z01630, z11397, z2931), z1, z2)) -> c17(A__U11(a__U11(mark(z01630), z11397, z2931), z1, z2), MARK(U11(z01630, z11397, z2931))) [1]
   MARK(U11(U12(z01631, z11398, z2932), z1, z2)) -> c17(A__U11(a__U12(mark(z01631), z11398, z2932), z1, z2), MARK(U12(z01631, z11398, z2932))) [1]
   MARK(U11(plus(z01632, z11399), z1, z2)) -> c17(A__U11(a__plus(mark(z01632), mark(z11399)), z1, z2), MARK(plus(z01632, z11399))) [1]
   MARK(U11(U21(z01633, z11400, z2933), z1, z2)) -> c17(A__U11(a__U21(mark(z01633), z11400, z2933), z1, z2), MARK(U21(z01633, z11400, z2933))) [1]
   MARK(U11(U22(z01634, z11401, z2934), z1, z2)) -> c17(A__U11(a__U22(mark(z01634), z11401, z2934), z1, z2), MARK(U22(z01634, z11401, z2934))) [1]
   MARK(U11(x(z01635, z11402), z1, z2)) -> c17(A__U11(a__x(mark(z01635), mark(z11402)), z1, z2), MARK(x(z01635, z11402))) [1]
   MARK(U11(tt, z1, z2)) -> c17(A__U11(tt, z1, z2), MARK(tt)) [1]
   MARK(U11(s(z01636), z1, z2)) -> c17(A__U11(s(mark(z01636)), z1, z2), MARK(s(z01636))) [1]
   MARK(U11(0, z1, z2)) -> c17(A__U11(0, z1, z2), MARK(0)) [1]
   MARK(U11(z0, z1, z2)) -> c17(A__U11(null_mark, z1, z2), MARK(z0)) [1]
   MARK(U12(U11(z01637, z11403, z2935), z1, z2)) -> c18(A__U12(a__U11(mark(z01637), z11403, z2935), z1, z2), MARK(U11(z01637, z11403, z2935))) [1]
   MARK(U12(U12(z01638, z11404, z2936), z1, z2)) -> c18(A__U12(a__U12(mark(z01638), z11404, z2936), z1, z2), MARK(U12(z01638, z11404, z2936))) [1]
   MARK(U12(plus(z01639, z11405), z1, z2)) -> c18(A__U12(a__plus(mark(z01639), mark(z11405)), z1, z2), MARK(plus(z01639, z11405))) [1]
   MARK(U12(U21(z01640, z11406, z2937), z1, z2)) -> c18(A__U12(a__U21(mark(z01640), z11406, z2937), z1, z2), MARK(U21(z01640, z11406, z2937))) [1]
   MARK(U12(U22(z01641, z11407, z2938), z1, z2)) -> c18(A__U12(a__U22(mark(z01641), z11407, z2938), z1, z2), MARK(U22(z01641, z11407, z2938))) [1]
   MARK(U12(x(z01642, z11408), z1, z2)) -> c18(A__U12(a__x(mark(z01642), mark(z11408)), z1, z2), MARK(x(z01642, z11408))) [1]
   MARK(U12(tt, z1, z2)) -> c18(A__U12(tt, z1, z2), MARK(tt)) [1]
   MARK(U12(s(z01643), z1, z2)) -> c18(A__U12(s(mark(z01643)), z1, z2), MARK(s(z01643))) [1]
   MARK(U12(0, z1, z2)) -> c18(A__U12(0, z1, z2), MARK(0)) [1]
   MARK(U12(z0, z1, z2)) -> c18(A__U12(null_mark, z1, z2), MARK(z0)) [1]
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(U21(U11(z01798, z11541, z21027), z1, z2)) -> c21(A__U21(a__U11(mark(z01798), z11541, z21027), z1, z2), MARK(U11(z01798, z11541, z21027))) [1]
   MARK(U21(U12(z01799, z11542, z21028), z1, z2)) -> c21(A__U21(a__U12(mark(z01799), z11542, z21028), z1, z2), MARK(U12(z01799, z11542, z21028))) [1]
   MARK(U21(plus(z01800, z11543), z1, z2)) -> c21(A__U21(a__plus(mark(z01800), mark(z11543)), z1, z2), MARK(plus(z01800, z11543))) [1]
   MARK(U21(U21(z01801, z11544, z21029), z1, z2)) -> c21(A__U21(a__U21(mark(z01801), z11544, z21029), z1, z2), MARK(U21(z01801, z11544, z21029))) [1]
   MARK(U21(U22(z01802, z11545, z21030), z1, z2)) -> c21(A__U21(a__U22(mark(z01802), z11545, z21030), z1, z2), MARK(U22(z01802, z11545, z21030))) [1]
   MARK(U21(x(z01803, z11546), z1, z2)) -> c21(A__U21(a__x(mark(z01803), mark(z11546)), z1, z2), MARK(x(z01803, z11546))) [1]
   MARK(U21(tt, z1, z2)) -> c21(A__U21(tt, z1, z2), MARK(tt)) [1]
   MARK(U21(s(z01804), z1, z2)) -> c21(A__U21(s(mark(z01804)), z1, z2), MARK(s(z01804))) [1]
   MARK(U21(0, z1, z2)) -> c21(A__U21(0, z1, z2), MARK(0)) [1]
   MARK(U21(z0, z1, z2)) -> c21(A__U21(null_mark, z1, z2), MARK(z0)) [1]
   MARK(U22(U11(z01805, z11547, z21031), z1, z2)) -> c22(A__U22(a__U11(mark(z01805), z11547, z21031), z1, z2), MARK(U11(z01805, z11547, z21031))) [1]
   MARK(U22(U12(z01806, z11548, z21032), z1, z2)) -> c22(A__U22(a__U12(mark(z01806), z11548, z21032), z1, z2), MARK(U12(z01806, z11548, z21032))) [1]
   MARK(U22(plus(z01807, z11549), z1, z2)) -> c22(A__U22(a__plus(mark(z01807), mark(z11549)), z1, z2), MARK(plus(z01807, z11549))) [1]
   MARK(U22(U21(z01808, z11550, z21033), z1, z2)) -> c22(A__U22(a__U21(mark(z01808), z11550, z21033), z1, z2), MARK(U21(z01808, z11550, z21033))) [1]
   MARK(U22(U22(z01809, z11551, z21034), z1, z2)) -> c22(A__U22(a__U22(mark(z01809), z11551, z21034), z1, z2), MARK(U22(z01809, z11551, z21034))) [1]
   MARK(U22(x(z01810, z11552), z1, z2)) -> c22(A__U22(a__x(mark(z01810), mark(z11552)), z1, z2), MARK(x(z01810, z11552))) [1]
   MARK(U22(tt, z1, z2)) -> c22(A__U22(tt, z1, z2), MARK(tt)) [1]
   MARK(U22(s(z01811), z1, z2)) -> c22(A__U22(s(mark(z01811)), z1, z2), MARK(s(z01811))) [1]
   MARK(U22(0, z1, z2)) -> c22(A__U22(0, z1, z2), MARK(0)) [1]
   MARK(U22(z0, z1, z2)) -> c22(A__U22(null_mark, z1, z2), MARK(z0)) [1]
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(s(z0)) -> c26(MARK(z0)) [1]
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) [0]
   a__U11(z0, z1, z2) -> U11(z0, z1, z2) [0]
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0]
   a__U12(z0, z1, z2) -> U12(z0, z1, z2) [0]
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1) [0]
   a__U21(z0, z1, z2) -> U21(z0, z1, z2) [0]
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) [0]
   a__U22(z0, z1, z2) -> U22(z0, z1, z2) [0]
   a__plus(z0, 0) -> mark(z0) [0]
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) [0]
   a__plus(z0, z1) -> plus(z0, z1) [0]
   a__x(z0, 0) -> 0 [0]
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0) [0]
   a__x(z0, z1) -> x(z0, z1) [0]
   mark(U11(U11(z02190, z11877, z21251), z1, z2)) -> a__U11(a__U11(mark(z02190), z11877, z21251), z1, z2) [0]
   mark(U11(U12(z02191, z11878, z21252), z1, z2)) -> a__U11(a__U12(mark(z02191), z11878, z21252), z1, z2) [0]
   mark(U11(plus(z02192, z11879), z1, z2)) -> a__U11(a__plus(mark(z02192), mark(z11879)), z1, z2) [0]
   mark(U11(U21(z02193, z11880, z21253), z1, z2)) -> a__U11(a__U21(mark(z02193), z11880, z21253), z1, z2) [0]
   mark(U11(U22(z02194, z11881, z21254), z1, z2)) -> a__U11(a__U22(mark(z02194), z11881, z21254), z1, z2) [0]
   mark(U11(x(z02195, z11882), z1, z2)) -> a__U11(a__x(mark(z02195), mark(z11882)), z1, z2) [0]
   mark(U11(tt, z1, z2)) -> a__U11(tt, z1, z2) [0]
   mark(U11(s(z02196), z1, z2)) -> a__U11(s(mark(z02196)), z1, z2) [0]
   mark(U11(0, z1, z2)) -> a__U11(0, z1, z2) [0]
   mark(U11(z0, z1, z2)) -> a__U11(null_mark, z1, z2) [0]
   mark(U12(U11(z02197, z11883, z21255), z1, z2)) -> a__U12(a__U11(mark(z02197), z11883, z21255), z1, z2) [0]
   mark(U12(U12(z02198, z11884, z21256), z1, z2)) -> a__U12(a__U12(mark(z02198), z11884, z21256), z1, z2) [0]
   mark(U12(plus(z02199, z11885), z1, z2)) -> a__U12(a__plus(mark(z02199), mark(z11885)), z1, z2) [0]
   mark(U12(U21(z02200, z11886, z21257), z1, z2)) -> a__U12(a__U21(mark(z02200), z11886, z21257), z1, z2) [0]
   mark(U12(U22(z02201, z11887, z21258), z1, z2)) -> a__U12(a__U22(mark(z02201), z11887, z21258), z1, z2) [0]
   mark(U12(x(z02202, z11888), z1, z2)) -> a__U12(a__x(mark(z02202), mark(z11888)), z1, z2) [0]
   mark(U12(tt, z1, z2)) -> a__U12(tt, z1, z2) [0]
   mark(U12(s(z02203), z1, z2)) -> a__U12(s(mark(z02203)), z1, z2) [0]
   mark(U12(0, z1, z2)) -> a__U12(0, z1, z2) [0]
   mark(U12(z0, z1, z2)) -> a__U12(null_mark, z1, z2) [0]
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0]
   mark(U21(U11(z02281, z11955, z21303), z1, z2)) -> a__U21(a__U11(mark(z02281), z11955, z21303), z1, z2) [0]
   mark(U21(U12(z02282, z11956, z21304), z1, z2)) -> a__U21(a__U12(mark(z02282), z11956, z21304), z1, z2) [0]
   mark(U21(plus(z02283, z11957), z1, z2)) -> a__U21(a__plus(mark(z02283), mark(z11957)), z1, z2) [0]
   mark(U21(U21(z02284, z11958, z21305), z1, z2)) -> a__U21(a__U21(mark(z02284), z11958, z21305), z1, z2) [0]
   mark(U21(U22(z02285, z11959, z21306), z1, z2)) -> a__U21(a__U22(mark(z02285), z11959, z21306), z1, z2) [0]
   mark(U21(x(z02286, z11960), z1, z2)) -> a__U21(a__x(mark(z02286), mark(z11960)), z1, z2) [0]
   mark(U21(tt, z1, z2)) -> a__U21(tt, z1, z2) [0]
   mark(U21(s(z02287), z1, z2)) -> a__U21(s(mark(z02287)), z1, z2) [0]
   mark(U21(0, z1, z2)) -> a__U21(0, z1, z2) [0]
   mark(U21(z0, z1, z2)) -> a__U21(null_mark, z1, z2) [0]
   mark(U22(U11(z02288, z11961, z21307), z1, z2)) -> a__U22(a__U11(mark(z02288), z11961, z21307), z1, z2) [0]
   mark(U22(U12(z02289, z11962, z21308), z1, z2)) -> a__U22(a__U12(mark(z02289), z11962, z21308), z1, z2) [0]
   mark(U22(plus(z02290, z11963), z1, z2)) -> a__U22(a__plus(mark(z02290), mark(z11963)), z1, z2) [0]
   mark(U22(U21(z02291, z11964, z21309), z1, z2)) -> a__U22(a__U21(mark(z02291), z11964, z21309), z1, z2) [0]
   mark(U22(U22(z02292, z11965, z21310), z1, z2)) -> a__U22(a__U22(mark(z02292), z11965, z21310), z1, z2) [0]
   mark(U22(x(z02293, z11966), z1, z2)) -> a__U22(a__x(mark(z02293), mark(z11966)), z1, z2) [0]
   mark(U22(tt, z1, z2)) -> a__U22(tt, z1, z2) [0]
   mark(U22(s(z02294), z1, z2)) -> a__U22(s(mark(z02294)), z1, z2) [0]
   mark(U22(0, z1, z2)) -> a__U22(0, z1, z2) [0]
   mark(U22(z0, z1, z2)) -> a__U22(null_mark, z1, z2) [0]
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) [0]
   mark(tt) -> tt [0]
   mark(s(z0)) -> s(mark(z0)) [0]
   mark(0) -> 0 [0]
   a__U11(v0, v1, v2) -> null_a__U11 [0]
   a__U12(v0, v1, v2) -> null_a__U12 [0]
   a__U21(v0, v1, v2) -> null_a__U21 [0]
   a__U22(v0, v1, v2) -> null_a__U22 [0]
   a__plus(v0, v1) -> null_a__plus [0]
   a__x(v0, v1) -> null_a__x [0]
   mark(v0) -> null_mark [0]

The TRS has the following type information:
A__U11 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> c
tt :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
c :: c2:c3 -> c
A__U12 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> c2:c3
c2 :: c11:c12 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c2:c3
A__PLUS :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> c11:c12
mark :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
MARK :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> c17:c18:c19:c20:c21:c22:c23:c24:c26
c3 :: c11:c12 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c2:c3
A__U21 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> c5
c5 :: c7:c8:c9 -> c5
A__U22 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> c7:c8:c9
c7 :: c11:c12 -> c15 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c7:c8:c9
a__x :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
A__X :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> c15
c8 :: c11:c12 -> c15 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c7:c8:c9
c9 :: c11:c12 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c7:c8:c9
0 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
c11 :: c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c11:c12
s :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
c12 :: c -> c11:c12
c15 :: c5 -> c15
U11 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
c17 :: c -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c17:c18:c19:c20:c21:c22:c23:c24:c26
U12 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
c18 :: c2:c3 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c17:c18:c19:c20:c21:c22:c23:c24:c26
plus :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
c19 :: c11:c12 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c17:c18:c19:c20:c21:c22:c23:c24:c26
c20 :: c11:c12 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c17:c18:c19:c20:c21:c22:c23:c24:c26
U21 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
c21 :: c5 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c17:c18:c19:c20:c21:c22:c23:c24:c26
U22 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
c22 :: c7:c8:c9 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c17:c18:c19:c20:c21:c22:c23:c24:c26
x :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
c23 :: c15 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c17:c18:c19:c20:c21:c22:c23:c24:c26
c24 :: c15 -> c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c17:c18:c19:c20:c21:c22:c23:c24:c26
c26 :: c17:c18:c19:c20:c21:c22:c23:c24:c26 -> c17:c18:c19:c20:c21:c22:c23:c24:c26
a__U11 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
a__U12 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
a__plus :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
a__U21 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
a__U22 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
null_a__U11 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
null_a__U12 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
null_a__U21 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
null_a__U22 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
null_a__plus :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
null_a__x :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
null_mark :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
const :: c
const1 :: c2:c3
const2 :: c11:c12
const3 :: c17:c18:c19:c20:c21:c22:c23:c24:c26
const4 :: c5
const5 :: c7:c8:c9
const6 :: c15

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

(75) 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
   null_a__U11 => 0
   null_a__U12 => 0
   null_a__U21 => 0
   null_a__U22 => 0
   null_a__plus => 0
   null_a__x => 0
   null_mark => 0
   const => 0
   const1 => 0
   const2 => 0
   const3 => 0
   const4 => 0
   const5 => 0
   const6 => 0

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

(76)
Obligation:
Complexity RNTS consisting of the following rules:

   A__PLUS(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = z0, z0 >= 0, z' = 0
   A__PLUS(z, z') -{ 1 }-> 1 + A__U11(1, z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1
   A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(1, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   A__U12(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   A__U12(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   A__U21(z, z', z'') -{ 1 }-> 1 + A__U22(1, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   A__U22(z, z', z'') -{ 1 }-> 1 + A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)) + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   A__U22(z, z', z'') -{ 1 }-> 1 + A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)) + A__X(mark(z1), mark(z0)) + MARK(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   A__U22(z, z', z'') -{ 1 }-> 1 + A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)) + A__X(mark(z1), mark(z0)) + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   A__X(z, z') -{ 1 }-> 1 + A__U21(1, z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1
   MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__X(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__X(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U22(a__x(mark(z01810), mark(z11552)), z1, z2) + MARK(1 + z01810 + z11552) :|: z01810 >= 0, z1 >= 0, z11552 >= 0, z = 1 + (1 + z01810 + z11552) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U22(a__plus(mark(z01807), mark(z11549)), z1, z2) + MARK(1 + z01807 + z11549) :|: z = 1 + (1 + z01807 + z11549) + z1 + z2, z01807 >= 0, z1 >= 0, z11549 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U22(a__U22(mark(z01809), z11551, z21034), z1, z2) + MARK(1 + z01809 + z11551 + z21034) :|: z1 >= 0, z01809 >= 0, z21034 >= 0, z11551 >= 0, z = 1 + (1 + z01809 + z11551 + z21034) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U22(a__U21(mark(z01808), z11550, z21033), z1, z2) + MARK(1 + z01808 + z11550 + z21033) :|: z01808 >= 0, z1 >= 0, z11550 >= 0, z = 1 + (1 + z01808 + z11550 + z21033) + z1 + z2, z21033 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U22(a__U12(mark(z01806), z11548, z21032), z1, z2) + MARK(1 + z01806 + z11548 + z21032) :|: z1 >= 0, z = 1 + (1 + z01806 + z11548 + z21032) + z1 + z2, z21032 >= 0, z11548 >= 0, z01806 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U22(a__U11(mark(z01805), z11547, z21031), z1, z2) + MARK(1 + z01805 + z11547 + z21031) :|: z21031 >= 0, z11547 >= 0, z1 >= 0, z = 1 + (1 + z01805 + z11547 + z21031) + z1 + z2, z01805 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U22(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U22(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U22(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U22(1 + mark(z01811), z1, z2) + MARK(1 + z01811) :|: z1 >= 0, z01811 >= 0, z = 1 + (1 + z01811) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U21(a__x(mark(z01803), mark(z11546)), z1, z2) + MARK(1 + z01803 + z11546) :|: z01803 >= 0, z1 >= 0, z = 1 + (1 + z01803 + z11546) + z1 + z2, z11546 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U21(a__plus(mark(z01800), mark(z11543)), z1, z2) + MARK(1 + z01800 + z11543) :|: z11543 >= 0, z1 >= 0, z01800 >= 0, z2 >= 0, z = 1 + (1 + z01800 + z11543) + z1 + z2
   MARK(z) -{ 1 }-> 1 + A__U21(a__U22(mark(z01802), z11545, z21030), z1, z2) + MARK(1 + z01802 + z11545 + z21030) :|: z1 >= 0, z01802 >= 0, z = 1 + (1 + z01802 + z11545 + z21030) + z1 + z2, z11545 >= 0, z2 >= 0, z21030 >= 0
   MARK(z) -{ 1 }-> 1 + A__U21(a__U21(mark(z01801), z11544, z21029), z1, z2) + MARK(1 + z01801 + z11544 + z21029) :|: z21029 >= 0, z1 >= 0, z01801 >= 0, z = 1 + (1 + z01801 + z11544 + z21029) + z1 + z2, z11544 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U21(a__U12(mark(z01799), z11542, z21028), z1, z2) + MARK(1 + z01799 + z11542 + z21028) :|: z01799 >= 0, z = 1 + (1 + z01799 + z11542 + z21028) + z1 + z2, z1 >= 0, z11542 >= 0, z2 >= 0, z21028 >= 0
   MARK(z) -{ 1 }-> 1 + A__U21(a__U11(mark(z01798), z11541, z21027), z1, z2) + MARK(1 + z01798 + z11541 + z21027) :|: z1 >= 0, z11541 >= 0, z = 1 + (1 + z01798 + z11541 + z21027) + z1 + z2, z21027 >= 0, z01798 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U21(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U21(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U21(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U21(1 + mark(z01804), z1, z2) + MARK(1 + z01804) :|: z01804 >= 0, z1 >= 0, z2 >= 0, z = 1 + (1 + z01804) + z1 + z2
   MARK(z) -{ 1 }-> 1 + A__U12(a__x(mark(z01642), mark(z11408)), z1, z2) + MARK(1 + z01642 + z11408) :|: z1 >= 0, z11408 >= 0, z01642 >= 0, z = 1 + (1 + z01642 + z11408) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U12(a__plus(mark(z01639), mark(z11405)), z1, z2) + MARK(1 + z01639 + z11405) :|: z = 1 + (1 + z01639 + z11405) + z1 + z2, z1 >= 0, z11405 >= 0, z01639 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U12(a__U22(mark(z01641), z11407, z2938), z1, z2) + MARK(1 + z01641 + z11407 + z2938) :|: z = 1 + (1 + z01641 + z11407 + z2938) + z1 + z2, z1 >= 0, z2938 >= 0, z01641 >= 0, z11407 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U12(a__U21(mark(z01640), z11406, z2937), z1, z2) + MARK(1 + z01640 + z11406 + z2937) :|: z11406 >= 0, z1 >= 0, z2937 >= 0, z = 1 + (1 + z01640 + z11406 + z2937) + z1 + z2, z2 >= 0, z01640 >= 0
   MARK(z) -{ 1 }-> 1 + A__U12(a__U12(mark(z01638), z11404, z2936), z1, z2) + MARK(1 + z01638 + z11404 + z2936) :|: z1 >= 0, z = 1 + (1 + z01638 + z11404 + z2936) + z1 + z2, z2936 >= 0, z11404 >= 0, z2 >= 0, z01638 >= 0
   MARK(z) -{ 1 }-> 1 + A__U12(a__U11(mark(z01637), z11403, z2935), z1, z2) + MARK(1 + z01637 + z11403 + z2935) :|: z01637 >= 0, z2935 >= 0, z1 >= 0, z = 1 + (1 + z01637 + z11403 + z2935) + z1 + z2, z11403 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U12(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U12(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U12(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U12(1 + mark(z01643), z1, z2) + MARK(1 + z01643) :|: z1 >= 0, z01643 >= 0, z = 1 + (1 + z01643) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(a__x(mark(z01635), mark(z11402)), z1, z2) + MARK(1 + z01635 + z11402) :|: z11402 >= 0, z1 >= 0, z = 1 + (1 + z01635 + z11402) + z1 + z2, z01635 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(a__plus(mark(z01632), mark(z11399)), z1, z2) + MARK(1 + z01632 + z11399) :|: z1 >= 0, z = 1 + (1 + z01632 + z11399) + z1 + z2, z11399 >= 0, z01632 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(a__U22(mark(z01634), z11401, z2934), z1, z2) + MARK(1 + z01634 + z11401 + z2934) :|: z1 >= 0, z11401 >= 0, z01634 >= 0, z = 1 + (1 + z01634 + z11401 + z2934) + z1 + z2, z2934 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(a__U21(mark(z01633), z11400, z2933), z1, z2) + MARK(1 + z01633 + z11400 + z2933) :|: z01633 >= 0, z1 >= 0, z11400 >= 0, z2933 >= 0, z = 1 + (1 + z01633 + z11400 + z2933) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(a__U12(mark(z01631), z11398, z2932), z1, z2) + MARK(1 + z01631 + z11398 + z2932) :|: z1 >= 0, z = 1 + (1 + z01631 + z11398 + z2932) + z1 + z2, z01631 >= 0, z11398 >= 0, z2 >= 0, z2932 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(a__U11(mark(z01630), z11397, z2931), z1, z2) + MARK(1 + z01630 + z11397 + z2931) :|: z11397 >= 0, z2931 >= 0, z1 >= 0, z = 1 + (1 + z01630 + z11397 + z2931) + z1 + z2, z2 >= 0, z01630 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(1 + mark(z01636), z1, z2) + MARK(1 + z01636) :|: z1 >= 0, z01636 >= 0, z = 1 + (1 + z01636) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__U11(z, z', z'') -{ 0 }-> a__U12(1, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   a__U11(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   a__U11(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0
   a__U12(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   a__U12(z, z', z'') -{ 0 }-> 1 + a__plus(mark(z1), mark(z0)) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   a__U12(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0
   a__U21(z, z', z'') -{ 0 }-> a__U22(1, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   a__U21(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   a__U21(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0
   a__U22(z, z', z'') -{ 0 }-> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   a__U22(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   a__U22(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0
   a__plus(z, z') -{ 0 }-> mark(z0) :|: z = z0, z0 >= 0, z' = 0
   a__plus(z, z') -{ 0 }-> a__U11(1, z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1
   a__plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__plus(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__x(z, z') -{ 0 }-> a__U21(1, z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1
   a__x(z, z') -{ 0 }-> 0 :|: z = z0, z0 >= 0, z' = 0
   a__x(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__x(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   mark(z) -{ 0 }-> a__x(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__plus(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U22(a__x(mark(z02293), mark(z11966)), z1, z2) :|: z1 >= 0, z11966 >= 0, z02293 >= 0, z2 >= 0, z = 1 + (1 + z02293 + z11966) + z1 + z2
   mark(z) -{ 0 }-> a__U22(a__plus(mark(z02290), mark(z11963)), z1, z2) :|: z11963 >= 0, z1 >= 0, z = 1 + (1 + z02290 + z11963) + z1 + z2, z02290 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U22(a__U22(mark(z02292), z11965, z21310), z1, z2) :|: z1 >= 0, z21310 >= 0, z11965 >= 0, z02292 >= 0, z = 1 + (1 + z02292 + z11965 + z21310) + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U22(a__U21(mark(z02291), z11964, z21309), z1, z2) :|: z02291 >= 0, z1 >= 0, z11964 >= 0, z21309 >= 0, z = 1 + (1 + z02291 + z11964 + z21309) + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U22(a__U12(mark(z02289), z11962, z21308), z1, z2) :|: z1 >= 0, z21308 >= 0, z = 1 + (1 + z02289 + z11962 + z21308) + z1 + z2, z02289 >= 0, z11962 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U22(a__U11(mark(z02288), z11961, z21307), z1, z2) :|: z02288 >= 0, z1 >= 0, z11961 >= 0, z21307 >= 0, z = 1 + (1 + z02288 + z11961 + z21307) + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U22(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U22(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U22(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U22(1 + mark(z02294), z1, z2) :|: z1 >= 0, z02294 >= 0, z = 1 + (1 + z02294) + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U21(a__x(mark(z02286), mark(z11960)), z1, z2) :|: z1 >= 0, z = 1 + (1 + z02286 + z11960) + z1 + z2, z02286 >= 0, z11960 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U21(a__plus(mark(z02283), mark(z11957)), z1, z2) :|: z = 1 + (1 + z02283 + z11957) + z1 + z2, z11957 >= 0, z1 >= 0, z02283 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U21(a__U22(mark(z02285), z11959, z21306), z1, z2) :|: z1 >= 0, z = 1 + (1 + z02285 + z11959 + z21306) + z1 + z2, z02285 >= 0, z21306 >= 0, z11959 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U21(a__U21(mark(z02284), z11958, z21305), z1, z2) :|: z02284 >= 0, z1 >= 0, z = 1 + (1 + z02284 + z11958 + z21305) + z1 + z2, z11958 >= 0, z21305 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U21(a__U12(mark(z02282), z11956, z21304), z1, z2) :|: z11956 >= 0, z1 >= 0, z02282 >= 0, z = 1 + (1 + z02282 + z11956 + z21304) + z1 + z2, z21304 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U21(a__U11(mark(z02281), z11955, z21303), z1, z2) :|: z = 1 + (1 + z02281 + z11955 + z21303) + z1 + z2, z1 >= 0, z11955 >= 0, z21303 >= 0, z02281 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U21(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U21(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U21(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U21(1 + mark(z02287), z1, z2) :|: z1 >= 0, z = 1 + (1 + z02287) + z1 + z2, z02287 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U12(a__x(mark(z02202), mark(z11888)), z1, z2) :|: z1 >= 0, z02202 >= 0, z11888 >= 0, z = 1 + (1 + z02202 + z11888) + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U12(a__plus(mark(z02199), mark(z11885)), z1, z2) :|: z11885 >= 0, z1 >= 0, z = 1 + (1 + z02199 + z11885) + z1 + z2, z02199 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U12(a__U22(mark(z02201), z11887, z21258), z1, z2) :|: z21258 >= 0, z1 >= 0, z = 1 + (1 + z02201 + z11887 + z21258) + z1 + z2, z11887 >= 0, z02201 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U12(a__U21(mark(z02200), z11886, z21257), z1, z2) :|: z1 >= 0, z11886 >= 0, z = 1 + (1 + z02200 + z11886 + z21257) + z1 + z2, z21257 >= 0, z2 >= 0, z02200 >= 0
   mark(z) -{ 0 }-> a__U12(a__U12(mark(z02198), z11884, z21256), z1, z2) :|: z1 >= 0, z21256 >= 0, z = 1 + (1 + z02198 + z11884 + z21256) + z1 + z2, z11884 >= 0, z02198 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U12(a__U11(mark(z02197), z11883, z21255), z1, z2) :|: z1 >= 0, z = 1 + (1 + z02197 + z11883 + z21255) + z1 + z2, z11883 >= 0, z02197 >= 0, z21255 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U12(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U12(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U12(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U12(1 + mark(z02203), z1, z2) :|: z = 1 + (1 + z02203) + z1 + z2, z1 >= 0, z02203 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U11(a__x(mark(z02195), mark(z11882)), z1, z2) :|: z1 >= 0, z = 1 + (1 + z02195 + z11882) + z1 + z2, z02195 >= 0, z2 >= 0, z11882 >= 0
   mark(z) -{ 0 }-> a__U11(a__plus(mark(z02192), mark(z11879)), z1, z2) :|: z02192 >= 0, z1 >= 0, z = 1 + (1 + z02192 + z11879) + z1 + z2, z11879 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U11(a__U22(mark(z02194), z11881, z21254), z1, z2) :|: z21254 >= 0, z11881 >= 0, z1 >= 0, z02194 >= 0, z2 >= 0, z = 1 + (1 + z02194 + z11881 + z21254) + z1 + z2
   mark(z) -{ 0 }-> a__U11(a__U21(mark(z02193), z11880, z21253), z1, z2) :|: z1 >= 0, z21253 >= 0, z02193 >= 0, z11880 >= 0, z = 1 + (1 + z02193 + z11880 + z21253) + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U11(a__U12(mark(z02191), z11878, z21252), z1, z2) :|: z11878 >= 0, z1 >= 0, z21252 >= 0, z = 1 + (1 + z02191 + z11878 + z21252) + z1 + z2, z02191 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U11(a__U11(mark(z02190), z11877, z21251), z1, z2) :|: z1 >= 0, z = 1 + (1 + z02190 + z11877 + z21251) + z1 + z2, z21251 >= 0, z02190 >= 0, z11877 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U11(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U11(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U11(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U11(1 + mark(z02196), z1, z2) :|: z02196 >= 0, z1 >= 0, z = 1 + (1 + z02196) + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> 1 :|: z = 1
   mark(z) -{ 0 }-> 0 :|: z = 0
   mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0


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

(78)
Obligation:
Complexity RNTS consisting of the following rules:

   A__PLUS(z, z') -{ 1 }-> 1 + MARK(z) :|: z >= 0, z' = 0
   A__PLUS(z, z') -{ 1 }-> 1 + A__U11(1, z' - 1, z) :|: z' - 1 >= 0, z >= 0
   A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(1, z', z'') :|: z'' >= 0, z = 1, z' >= 0
   A__U12(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z''), mark(z')) + MARK(z') :|: z'' >= 0, z = 1, z' >= 0
   A__U12(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z''), mark(z')) + MARK(z'') :|: z'' >= 0, z = 1, z' >= 0
   A__U21(z, z', z'') -{ 1 }-> 1 + A__U22(1, z', z'') :|: z'' >= 0, z = 1, z' >= 0
   A__U22(z, z', z'') -{ 1 }-> 1 + A__PLUS(a__x(mark(z''), mark(z')), mark(z'')) + MARK(z'') :|: z'' >= 0, z = 1, z' >= 0
   A__U22(z, z', z'') -{ 1 }-> 1 + A__PLUS(a__x(mark(z''), mark(z')), mark(z'')) + A__X(mark(z''), mark(z')) + MARK(z') :|: z'' >= 0, z = 1, z' >= 0
   A__U22(z, z', z'') -{ 1 }-> 1 + A__PLUS(a__x(mark(z''), mark(z')), mark(z'')) + A__X(mark(z''), mark(z')) + MARK(z'') :|: z'' >= 0, z = 1, z' >= 0
   A__X(z, z') -{ 1 }-> 1 + A__U21(1, z' - 1, z) :|: z' - 1 >= 0, z >= 0
   MARK(z) -{ 1 }-> 1 + MARK(z - 1) :|: z - 1 >= 0
   MARK(z) -{ 1 }-> 1 + A__X(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__X(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U22(a__x(mark(z01810), mark(z11552)), z1, z2) + MARK(1 + z01810 + z11552) :|: z01810 >= 0, z1 >= 0, z11552 >= 0, z = 1 + (1 + z01810 + z11552) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U22(a__plus(mark(z01807), mark(z11549)), z1, z2) + MARK(1 + z01807 + z11549) :|: z = 1 + (1 + z01807 + z11549) + z1 + z2, z01807 >= 0, z1 >= 0, z11549 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U22(a__U22(mark(z01809), z11551, z21034), z1, z2) + MARK(1 + z01809 + z11551 + z21034) :|: z1 >= 0, z01809 >= 0, z21034 >= 0, z11551 >= 0, z = 1 + (1 + z01809 + z11551 + z21034) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U22(a__U21(mark(z01808), z11550, z21033), z1, z2) + MARK(1 + z01808 + z11550 + z21033) :|: z01808 >= 0, z1 >= 0, z11550 >= 0, z = 1 + (1 + z01808 + z11550 + z21033) + z1 + z2, z21033 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U22(a__U12(mark(z01806), z11548, z21032), z1, z2) + MARK(1 + z01806 + z11548 + z21032) :|: z1 >= 0, z = 1 + (1 + z01806 + z11548 + z21032) + z1 + z2, z21032 >= 0, z11548 >= 0, z01806 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U22(a__U11(mark(z01805), z11547, z21031), z1, z2) + MARK(1 + z01805 + z11547 + z21031) :|: z21031 >= 0, z11547 >= 0, z1 >= 0, z = 1 + (1 + z01805 + z11547 + z21031) + z1 + z2, z01805 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U22(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U22(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U22(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U22(1 + mark(z01811), z1, z2) + MARK(1 + z01811) :|: z1 >= 0, z01811 >= 0, z = 1 + (1 + z01811) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U21(a__x(mark(z01803), mark(z11546)), z1, z2) + MARK(1 + z01803 + z11546) :|: z01803 >= 0, z1 >= 0, z = 1 + (1 + z01803 + z11546) + z1 + z2, z11546 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U21(a__plus(mark(z01800), mark(z11543)), z1, z2) + MARK(1 + z01800 + z11543) :|: z11543 >= 0, z1 >= 0, z01800 >= 0, z2 >= 0, z = 1 + (1 + z01800 + z11543) + z1 + z2
   MARK(z) -{ 1 }-> 1 + A__U21(a__U22(mark(z01802), z11545, z21030), z1, z2) + MARK(1 + z01802 + z11545 + z21030) :|: z1 >= 0, z01802 >= 0, z = 1 + (1 + z01802 + z11545 + z21030) + z1 + z2, z11545 >= 0, z2 >= 0, z21030 >= 0
   MARK(z) -{ 1 }-> 1 + A__U21(a__U21(mark(z01801), z11544, z21029), z1, z2) + MARK(1 + z01801 + z11544 + z21029) :|: z21029 >= 0, z1 >= 0, z01801 >= 0, z = 1 + (1 + z01801 + z11544 + z21029) + z1 + z2, z11544 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U21(a__U12(mark(z01799), z11542, z21028), z1, z2) + MARK(1 + z01799 + z11542 + z21028) :|: z01799 >= 0, z = 1 + (1 + z01799 + z11542 + z21028) + z1 + z2, z1 >= 0, z11542 >= 0, z2 >= 0, z21028 >= 0
   MARK(z) -{ 1 }-> 1 + A__U21(a__U11(mark(z01798), z11541, z21027), z1, z2) + MARK(1 + z01798 + z11541 + z21027) :|: z1 >= 0, z11541 >= 0, z = 1 + (1 + z01798 + z11541 + z21027) + z1 + z2, z21027 >= 0, z01798 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U21(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U21(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U21(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U21(1 + mark(z01804), z1, z2) + MARK(1 + z01804) :|: z01804 >= 0, z1 >= 0, z2 >= 0, z = 1 + (1 + z01804) + z1 + z2
   MARK(z) -{ 1 }-> 1 + A__U12(a__x(mark(z01642), mark(z11408)), z1, z2) + MARK(1 + z01642 + z11408) :|: z1 >= 0, z11408 >= 0, z01642 >= 0, z = 1 + (1 + z01642 + z11408) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U12(a__plus(mark(z01639), mark(z11405)), z1, z2) + MARK(1 + z01639 + z11405) :|: z = 1 + (1 + z01639 + z11405) + z1 + z2, z1 >= 0, z11405 >= 0, z01639 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U12(a__U22(mark(z01641), z11407, z2938), z1, z2) + MARK(1 + z01641 + z11407 + z2938) :|: z = 1 + (1 + z01641 + z11407 + z2938) + z1 + z2, z1 >= 0, z2938 >= 0, z01641 >= 0, z11407 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U12(a__U21(mark(z01640), z11406, z2937), z1, z2) + MARK(1 + z01640 + z11406 + z2937) :|: z11406 >= 0, z1 >= 0, z2937 >= 0, z = 1 + (1 + z01640 + z11406 + z2937) + z1 + z2, z2 >= 0, z01640 >= 0
   MARK(z) -{ 1 }-> 1 + A__U12(a__U12(mark(z01638), z11404, z2936), z1, z2) + MARK(1 + z01638 + z11404 + z2936) :|: z1 >= 0, z = 1 + (1 + z01638 + z11404 + z2936) + z1 + z2, z2936 >= 0, z11404 >= 0, z2 >= 0, z01638 >= 0
   MARK(z) -{ 1 }-> 1 + A__U12(a__U11(mark(z01637), z11403, z2935), z1, z2) + MARK(1 + z01637 + z11403 + z2935) :|: z01637 >= 0, z2935 >= 0, z1 >= 0, z = 1 + (1 + z01637 + z11403 + z2935) + z1 + z2, z11403 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U12(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U12(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U12(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U12(1 + mark(z01643), z1, z2) + MARK(1 + z01643) :|: z1 >= 0, z01643 >= 0, z = 1 + (1 + z01643) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(a__x(mark(z01635), mark(z11402)), z1, z2) + MARK(1 + z01635 + z11402) :|: z11402 >= 0, z1 >= 0, z = 1 + (1 + z01635 + z11402) + z1 + z2, z01635 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(a__plus(mark(z01632), mark(z11399)), z1, z2) + MARK(1 + z01632 + z11399) :|: z1 >= 0, z = 1 + (1 + z01632 + z11399) + z1 + z2, z11399 >= 0, z01632 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(a__U22(mark(z01634), z11401, z2934), z1, z2) + MARK(1 + z01634 + z11401 + z2934) :|: z1 >= 0, z11401 >= 0, z01634 >= 0, z = 1 + (1 + z01634 + z11401 + z2934) + z1 + z2, z2934 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(a__U21(mark(z01633), z11400, z2933), z1, z2) + MARK(1 + z01633 + z11400 + z2933) :|: z01633 >= 0, z1 >= 0, z11400 >= 0, z2933 >= 0, z = 1 + (1 + z01633 + z11400 + z2933) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(a__U12(mark(z01631), z11398, z2932), z1, z2) + MARK(1 + z01631 + z11398 + z2932) :|: z1 >= 0, z = 1 + (1 + z01631 + z11398 + z2932) + z1 + z2, z01631 >= 0, z11398 >= 0, z2 >= 0, z2932 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(a__U11(mark(z01630), z11397, z2931), z1, z2) + MARK(1 + z01630 + z11397 + z2931) :|: z11397 >= 0, z2931 >= 0, z1 >= 0, z = 1 + (1 + z01630 + z11397 + z2931) + z1 + z2, z2 >= 0, z01630 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(1 + mark(z01636), z1, z2) + MARK(1 + z01636) :|: z1 >= 0, z01636 >= 0, z = 1 + (1 + z01636) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__U11(z, z', z'') -{ 0 }-> a__U12(1, z', z'') :|: z'' >= 0, z = 1, z' >= 0
   a__U11(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   a__U11(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0
   a__U12(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   a__U12(z, z', z'') -{ 0 }-> 1 + a__plus(mark(z''), mark(z')) :|: z'' >= 0, z = 1, z' >= 0
   a__U12(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0
   a__U21(z, z', z'') -{ 0 }-> a__U22(1, z', z'') :|: z'' >= 0, z = 1, z' >= 0
   a__U21(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   a__U21(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0
   a__U22(z, z', z'') -{ 0 }-> a__plus(a__x(mark(z''), mark(z')), mark(z'')) :|: z'' >= 0, z = 1, z' >= 0
   a__U22(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   a__U22(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0
   a__plus(z, z') -{ 0 }-> mark(z) :|: z >= 0, z' = 0
   a__plus(z, z') -{ 0 }-> a__U11(1, z' - 1, z) :|: z' - 1 >= 0, z >= 0
   a__plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   a__plus(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   a__x(z, z') -{ 0 }-> a__U21(1, z' - 1, z) :|: z' - 1 >= 0, z >= 0
   a__x(z, z') -{ 0 }-> 0 :|: z >= 0, z' = 0
   a__x(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   a__x(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   mark(z) -{ 0 }-> a__x(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__plus(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U22(a__x(mark(z02293), mark(z11966)), z1, z2) :|: z1 >= 0, z11966 >= 0, z02293 >= 0, z2 >= 0, z = 1 + (1 + z02293 + z11966) + z1 + z2
   mark(z) -{ 0 }-> a__U22(a__plus(mark(z02290), mark(z11963)), z1, z2) :|: z11963 >= 0, z1 >= 0, z = 1 + (1 + z02290 + z11963) + z1 + z2, z02290 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U22(a__U22(mark(z02292), z11965, z21310), z1, z2) :|: z1 >= 0, z21310 >= 0, z11965 >= 0, z02292 >= 0, z = 1 + (1 + z02292 + z11965 + z21310) + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U22(a__U21(mark(z02291), z11964, z21309), z1, z2) :|: z02291 >= 0, z1 >= 0, z11964 >= 0, z21309 >= 0, z = 1 + (1 + z02291 + z11964 + z21309) + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U22(a__U12(mark(z02289), z11962, z21308), z1, z2) :|: z1 >= 0, z21308 >= 0, z = 1 + (1 + z02289 + z11962 + z21308) + z1 + z2, z02289 >= 0, z11962 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U22(a__U11(mark(z02288), z11961, z21307), z1, z2) :|: z02288 >= 0, z1 >= 0, z11961 >= 0, z21307 >= 0, z = 1 + (1 + z02288 + z11961 + z21307) + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U22(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U22(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U22(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U22(1 + mark(z02294), z1, z2) :|: z1 >= 0, z02294 >= 0, z = 1 + (1 + z02294) + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U21(a__x(mark(z02286), mark(z11960)), z1, z2) :|: z1 >= 0, z = 1 + (1 + z02286 + z11960) + z1 + z2, z02286 >= 0, z11960 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U21(a__plus(mark(z02283), mark(z11957)), z1, z2) :|: z = 1 + (1 + z02283 + z11957) + z1 + z2, z11957 >= 0, z1 >= 0, z02283 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U21(a__U22(mark(z02285), z11959, z21306), z1, z2) :|: z1 >= 0, z = 1 + (1 + z02285 + z11959 + z21306) + z1 + z2, z02285 >= 0, z21306 >= 0, z11959 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U21(a__U21(mark(z02284), z11958, z21305), z1, z2) :|: z02284 >= 0, z1 >= 0, z = 1 + (1 + z02284 + z11958 + z21305) + z1 + z2, z11958 >= 0, z21305 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U21(a__U12(mark(z02282), z11956, z21304), z1, z2) :|: z11956 >= 0, z1 >= 0, z02282 >= 0, z = 1 + (1 + z02282 + z11956 + z21304) + z1 + z2, z21304 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U21(a__U11(mark(z02281), z11955, z21303), z1, z2) :|: z = 1 + (1 + z02281 + z11955 + z21303) + z1 + z2, z1 >= 0, z11955 >= 0, z21303 >= 0, z02281 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U21(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U21(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U21(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U21(1 + mark(z02287), z1, z2) :|: z1 >= 0, z = 1 + (1 + z02287) + z1 + z2, z02287 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U12(a__x(mark(z02202), mark(z11888)), z1, z2) :|: z1 >= 0, z02202 >= 0, z11888 >= 0, z = 1 + (1 + z02202 + z11888) + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U12(a__plus(mark(z02199), mark(z11885)), z1, z2) :|: z11885 >= 0, z1 >= 0, z = 1 + (1 + z02199 + z11885) + z1 + z2, z02199 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U12(a__U22(mark(z02201), z11887, z21258), z1, z2) :|: z21258 >= 0, z1 >= 0, z = 1 + (1 + z02201 + z11887 + z21258) + z1 + z2, z11887 >= 0, z02201 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U12(a__U21(mark(z02200), z11886, z21257), z1, z2) :|: z1 >= 0, z11886 >= 0, z = 1 + (1 + z02200 + z11886 + z21257) + z1 + z2, z21257 >= 0, z2 >= 0, z02200 >= 0
   mark(z) -{ 0 }-> a__U12(a__U12(mark(z02198), z11884, z21256), z1, z2) :|: z1 >= 0, z21256 >= 0, z = 1 + (1 + z02198 + z11884 + z21256) + z1 + z2, z11884 >= 0, z02198 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U12(a__U11(mark(z02197), z11883, z21255), z1, z2) :|: z1 >= 0, z = 1 + (1 + z02197 + z11883 + z21255) + z1 + z2, z11883 >= 0, z02197 >= 0, z21255 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U12(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U12(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U12(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U12(1 + mark(z02203), z1, z2) :|: z = 1 + (1 + z02203) + z1 + z2, z1 >= 0, z02203 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U11(a__x(mark(z02195), mark(z11882)), z1, z2) :|: z1 >= 0, z = 1 + (1 + z02195 + z11882) + z1 + z2, z02195 >= 0, z2 >= 0, z11882 >= 0
   mark(z) -{ 0 }-> a__U11(a__plus(mark(z02192), mark(z11879)), z1, z2) :|: z02192 >= 0, z1 >= 0, z = 1 + (1 + z02192 + z11879) + z1 + z2, z11879 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U11(a__U22(mark(z02194), z11881, z21254), z1, z2) :|: z21254 >= 0, z11881 >= 0, z1 >= 0, z02194 >= 0, z2 >= 0, z = 1 + (1 + z02194 + z11881 + z21254) + z1 + z2
   mark(z) -{ 0 }-> a__U11(a__U21(mark(z02193), z11880, z21253), z1, z2) :|: z1 >= 0, z21253 >= 0, z02193 >= 0, z11880 >= 0, z = 1 + (1 + z02193 + z11880 + z21253) + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U11(a__U12(mark(z02191), z11878, z21252), z1, z2) :|: z11878 >= 0, z1 >= 0, z21252 >= 0, z = 1 + (1 + z02191 + z11878 + z21252) + z1 + z2, z02191 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U11(a__U11(mark(z02190), z11877, z21251), z1, z2) :|: z1 >= 0, z = 1 + (1 + z02190 + z11877 + z21251) + z1 + z2, z21251 >= 0, z02190 >= 0, z11877 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U11(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U11(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U11(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U11(1 + mark(z02196), z1, z2) :|: z02196 >= 0, z1 >= 0, z = 1 + (1 + z02196) + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> 1 :|: z = 1
   mark(z) -{ 0 }-> 0 :|: z = 0
   mark(z) -{ 0 }-> 0 :|: z >= 0
   mark(z) -{ 0 }-> 1 + mark(z - 1) :|: z - 1 >= 0


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

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

   a__U11(v0, v1, v2) -> null_a__U11 [0]
   a__U12(v0, v1, v2) -> null_a__U12 [0]
   a__U21(v0, v1, v2) -> null_a__U21 [0]
   a__U22(v0, v1, v2) -> null_a__U22 [0]
   a__plus(v0, v1) -> null_a__plus [0]
   a__x(v0, v1) -> null_a__x [0]
   mark(v0) -> null_mark [0]
   A__U11(v0, v1, v2) -> null_A__U11 [0]
   A__U12(v0, v1, v2) -> null_A__U12 [0]
   A__U21(v0, v1, v2) -> null_A__U21 [0]
   A__U22(v0, v1, v2) -> null_A__U22 [0]
   A__PLUS(v0, v1) -> null_A__PLUS [0]
   A__X(v0, v1) -> null_A__X [0]
   MARK(v0) -> null_MARK [0]

And the following fresh constants:    null_a__U11, null_a__U12, null_a__U21, null_a__U22, null_a__plus, null_a__x, null_mark, null_A__U11, null_A__U12, null_A__U21, null_A__U22, null_A__PLUS, null_A__X, null_MARK

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

(80)
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, z0, z1) -> c(A__U12(tt, z0, z1)) [1]
   A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1]
   A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1]
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1)) [1]
   A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) [1]
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) [1]
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) [1]
   A__PLUS(z0, 0) -> c11(MARK(z0)) [1]
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0)) [1]
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0)) [1]
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(s(z0)) -> c26(MARK(z0)) [1]
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1) [0]
   a__U11(z0, z1, z2) -> U11(z0, z1, z2) [0]
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0]
   a__U12(z0, z1, z2) -> U12(z0, z1, z2) [0]
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1) [0]
   a__U21(z0, z1, z2) -> U21(z0, z1, z2) [0]
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) [0]
   a__U22(z0, z1, z2) -> U22(z0, z1, z2) [0]
   a__plus(z0, 0) -> mark(z0) [0]
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0) [0]
   a__plus(z0, z1) -> plus(z0, z1) [0]
   a__x(z0, 0) -> 0 [0]
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0) [0]
   a__x(z0, z1) -> x(z0, z1) [0]
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2) [0]
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2) [0]
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0]
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2) [0]
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2) [0]
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) [0]
   mark(tt) -> tt [0]
   mark(s(z0)) -> s(mark(z0)) [0]
   mark(0) -> 0 [0]
   a__U11(v0, v1, v2) -> null_a__U11 [0]
   a__U12(v0, v1, v2) -> null_a__U12 [0]
   a__U21(v0, v1, v2) -> null_a__U21 [0]
   a__U22(v0, v1, v2) -> null_a__U22 [0]
   a__plus(v0, v1) -> null_a__plus [0]
   a__x(v0, v1) -> null_a__x [0]
   mark(v0) -> null_mark [0]
   A__U11(v0, v1, v2) -> null_A__U11 [0]
   A__U12(v0, v1, v2) -> null_A__U12 [0]
   A__U21(v0, v1, v2) -> null_A__U21 [0]
   A__U22(v0, v1, v2) -> null_A__U22 [0]
   A__PLUS(v0, v1) -> null_A__PLUS [0]
   A__X(v0, v1) -> null_A__X [0]
   MARK(v0) -> null_MARK [0]

The TRS has the following type information:
A__U11 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> c:null_A__U11
tt :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
c :: c2:c3:null_A__U12 -> c:null_A__U11
A__U12 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> c2:c3:null_A__U12
c2 :: c11:c12:null_A__PLUS -> c17:c18:c19:c20:c21:c22:c23:c24:c26:null_MARK -> c2:c3:null_A__U12
A__PLUS :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> c11:c12:null_A__PLUS
mark :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
MARK :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> c17:c18:c19:c20:c21:c22:c23:c24:c26:null_MARK
c3 :: c11:c12:null_A__PLUS -> c17:c18:c19:c20:c21:c22:c23:c24:c26:null_MARK -> c2:c3:null_A__U12
A__U21 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> c5:null_A__U21
c5 :: c7:c8:c9:null_A__U22 -> c5:null_A__U21
A__U22 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> c7:c8:c9:null_A__U22
c7 :: c11:c12:null_A__PLUS -> c15:null_A__X -> c17:c18:c19:c20:c21:c22:c23:c24:c26:null_MARK -> c7:c8:c9:null_A__U22
a__x :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
A__X :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> c15:null_A__X
c8 :: c11:c12:null_A__PLUS -> c15:null_A__X -> c17:c18:c19:c20:c21:c22:c23:c24:c26:null_MARK -> c7:c8:c9:null_A__U22
c9 :: c11:c12:null_A__PLUS -> c17:c18:c19:c20:c21:c22:c23:c24:c26:null_MARK -> c7:c8:c9:null_A__U22
0 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
c11 :: c17:c18:c19:c20:c21:c22:c23:c24:c26:null_MARK -> c11:c12:null_A__PLUS
s :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
c12 :: c:null_A__U11 -> c11:c12:null_A__PLUS
c15 :: c5:null_A__U21 -> c15:null_A__X
U11 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
c17 :: c:null_A__U11 -> c17:c18:c19:c20:c21:c22:c23:c24:c26:null_MARK -> c17:c18:c19:c20:c21:c22:c23:c24:c26:null_MARK
U12 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
c18 :: c2:c3:null_A__U12 -> c17:c18:c19:c20:c21:c22:c23:c24:c26:null_MARK -> c17:c18:c19:c20:c21:c22:c23:c24:c26:null_MARK
plus :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
c19 :: c11:c12:null_A__PLUS -> c17:c18:c19:c20:c21:c22:c23:c24:c26:null_MARK -> c17:c18:c19:c20:c21:c22:c23:c24:c26:null_MARK
c20 :: c11:c12:null_A__PLUS -> c17:c18:c19:c20:c21:c22:c23:c24:c26:null_MARK -> c17:c18:c19:c20:c21:c22:c23:c24:c26:null_MARK
U21 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
c21 :: c5:null_A__U21 -> c17:c18:c19:c20:c21:c22:c23:c24:c26:null_MARK -> c17:c18:c19:c20:c21:c22:c23:c24:c26:null_MARK
U22 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
c22 :: c7:c8:c9:null_A__U22 -> c17:c18:c19:c20:c21:c22:c23:c24:c26:null_MARK -> c17:c18:c19:c20:c21:c22:c23:c24:c26:null_MARK
x :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
c23 :: c15:null_A__X -> c17:c18:c19:c20:c21:c22:c23:c24:c26:null_MARK -> c17:c18:c19:c20:c21:c22:c23:c24:c26:null_MARK
c24 :: c15:null_A__X -> c17:c18:c19:c20:c21:c22:c23:c24:c26:null_MARK -> c17:c18:c19:c20:c21:c22:c23:c24:c26:null_MARK
c26 :: c17:c18:c19:c20:c21:c22:c23:c24:c26:null_MARK -> c17:c18:c19:c20:c21:c22:c23:c24:c26:null_MARK
a__U11 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
a__U12 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
a__plus :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
a__U21 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
a__U22 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark -> tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
null_a__U11 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
null_a__U12 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
null_a__U21 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
null_a__U22 :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
null_a__plus :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
null_a__x :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
null_mark :: tt:0:s:U11:U12:plus:U21:U22:x:null_a__U11:null_a__U12:null_a__U21:null_a__U22:null_a__plus:null_a__x:null_mark
null_A__U11 :: c:null_A__U11
null_A__U12 :: c2:c3:null_A__U12
null_A__U21 :: c5:null_A__U21
null_A__U22 :: c7:c8:c9:null_A__U22
null_A__PLUS :: c11:c12:null_A__PLUS
null_A__X :: c15:null_A__X
null_MARK :: c17:c18:c19:c20:c21:c22:c23:c24:c26:null_MARK

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

(81) 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
   null_a__U11 => 0
   null_a__U12 => 0
   null_a__U21 => 0
   null_a__U22 => 0
   null_a__plus => 0
   null_a__x => 0
   null_mark => 0
   null_A__U11 => 0
   null_A__U12 => 0
   null_A__U21 => 0
   null_A__U22 => 0
   null_A__PLUS => 0
   null_A__X => 0
   null_MARK => 0

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

(82)
Obligation:
Complexity RNTS consisting of the following rules:

   A__PLUS(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   A__PLUS(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = z0, z0 >= 0, z' = 0
   A__PLUS(z, z') -{ 1 }-> 1 + A__U11(1, z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1
   A__U11(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   A__U11(z, z', z'') -{ 1 }-> 1 + A__U12(1, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   A__U12(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   A__U12(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   A__U12(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   A__U21(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   A__U21(z, z', z'') -{ 1 }-> 1 + A__U22(1, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   A__U22(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   A__U22(z, z', z'') -{ 1 }-> 1 + A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)) + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   A__U22(z, z', z'') -{ 1 }-> 1 + A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)) + A__X(mark(z1), mark(z0)) + MARK(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   A__U22(z, z', z'') -{ 1 }-> 1 + A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)) + A__X(mark(z1), mark(z0)) + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   A__X(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   A__X(z, z') -{ 1 }-> 1 + A__U21(1, z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1
   MARK(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__X(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__X(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U22(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U21(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U12(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__U11(z, z', z'') -{ 0 }-> a__U12(1, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   a__U11(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   a__U11(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0
   a__U12(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   a__U12(z, z', z'') -{ 0 }-> 1 + a__plus(mark(z1), mark(z0)) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   a__U12(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0
   a__U21(z, z', z'') -{ 0 }-> a__U22(1, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   a__U21(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   a__U21(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0
   a__U22(z, z', z'') -{ 0 }-> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   a__U22(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   a__U22(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0
   a__plus(z, z') -{ 0 }-> mark(z0) :|: z = z0, z0 >= 0, z' = 0
   a__plus(z, z') -{ 0 }-> a__U11(1, z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1
   a__plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__plus(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__x(z, z') -{ 0 }-> a__U21(1, z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1
   a__x(z, z') -{ 0 }-> 0 :|: z = z0, z0 >= 0, z' = 0
   a__x(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__x(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   mark(z) -{ 0 }-> a__x(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__plus(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U22(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U21(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U12(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U11(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> 1 :|: z = 1
   mark(z) -{ 0 }-> 0 :|: z = 0
   mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0

Only complete derivations are relevant for the runtime complexity.

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

(83) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, z0, z1) -> c2(A__PLUS(mark(z1), mark(z0)), MARK(z1)) by 
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, tt, x1) -> c2(A__PLUS(mark(x1), tt), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)), MARK(tt))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)), MARK(0))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, tt, x1) -> c2(A__PLUS(mark(x1), tt), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)), MARK(tt))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)), MARK(0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, tt, x1) -> c2(A__PLUS(mark(x1), tt), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)), MARK(tt))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U12_3, A__U21_3, A__U22_3, A__PLUS_2, A__X_2, MARK_1

Compound Symbols:   c_1, c3_2, c5_1, c7_3, c8_3, c9_2, c11_1, c12_1, c15_1, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c26_1, c2_2


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

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U12_3, A__U21_3, A__U22_3, A__PLUS_2, A__X_2, MARK_1

Compound Symbols:   c_1, c3_2, c5_1, c7_3, c8_3, c9_2, c11_1, c12_1, c15_1, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c26_1, c2_2, c2_1


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

(87) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, z0, z1) -> c3(A__PLUS(mark(z1), mark(z0)), MARK(z0)) by 
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, tt, x1) -> c3(A__PLUS(mark(x1), tt), MARK(tt))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0), MARK(0))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, tt, x1) -> c3(A__PLUS(mark(x1), tt), MARK(tt))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0), MARK(0))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, tt, x1) -> c3(A__PLUS(mark(x1), tt), MARK(tt))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0), MARK(0))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__U22_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3

Compound Symbols:   c_1, c5_1, c7_3, c8_3, c9_2, c11_1, c12_1, c15_1, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c26_1, c2_2, c2_1, c3_2


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

(89) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   A__U12(tt, tt, x1) -> c3(A__PLUS(mark(x1), tt), MARK(tt))

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0), MARK(0))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0), MARK(0))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__U22_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3

Compound Symbols:   c_1, c5_1, c7_3, c8_3, c9_2, c11_1, c12_1, c15_1, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c26_1, c2_2, c2_1, c3_2


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

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1))
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__U22_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3

Compound Symbols:   c_1, c5_1, c7_3, c8_3, c9_2, c11_1, c12_1, c15_1, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c26_1, c2_2, c2_1, c3_2, c3_1


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

(93) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U22(tt, z0, z1) -> c7(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) by 
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(mark(tt), mark(x0)), tt), A__X(mark(tt), mark(x0)), MARK(tt))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(0))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(tt))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(0))

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(mark(tt), mark(x0)), tt), A__X(mark(tt), mark(x0)), MARK(tt))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(0))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(tt))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(mark(tt), mark(x0)), tt), A__X(mark(tt), mark(x0)), MARK(tt))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(0))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(tt))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__U22_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3

Compound Symbols:   c_1, c5_1, c8_3, c9_2, c11_1, c12_1, c15_1, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3


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

(95) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 5 trailing tuple parts
----------------------------------------

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0))
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__U22_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3

Compound Symbols:   c_1, c5_1, c8_3, c9_2, c11_1, c12_1, c15_1, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2


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

(97) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U22(tt, z0, z1) -> c8(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) by 
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(mark(tt), mark(x0)), tt), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(tt))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(mark(tt), mark(x0)), tt), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(tt))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(mark(tt), mark(x0)), tt), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(tt))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__U22_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3

Compound Symbols:   c_1, c5_1, c9_2, c11_1, c12_1, c15_1, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3


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

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__U22_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3

Compound Symbols:   c_1, c5_1, c9_2, c11_1, c12_1, c15_1, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2


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

(101) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U22(tt, z0, z1) -> c9(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) by 
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(mark(tt), mark(x0)), tt), MARK(tt))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0), MARK(0))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)), MARK(tt))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)), MARK(0))

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(mark(tt), mark(x0)), tt), MARK(tt))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0), MARK(0))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)), MARK(tt))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)), MARK(0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(mark(tt), mark(x0)), tt), MARK(tt))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0), MARK(0))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)), MARK(tt))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2


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

(103) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(mark(tt), mark(x0)), tt), MARK(tt))

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

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0), MARK(0))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)), MARK(tt))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)), MARK(0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0), MARK(0))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)), MARK(tt))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2


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

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c17_2, c18_2, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1


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

(107) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(U11(z0, z1, z2)) -> c17(A__U11(mark(z0), z1, z2), MARK(z0)) by 
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2), MARK(tt))
   MARK(U11(s(z0), x1, x2)) -> c17(A__U11(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U11(0, x1, x2)) -> c17(A__U11(0, x1, x2), MARK(0))

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

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2), MARK(tt))
   MARK(U11(s(z0), x1, x2)) -> c17(A__U11(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U11(0, x1, x2)) -> c17(A__U11(0, x1, x2), MARK(0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2), MARK(tt))
   MARK(U11(s(z0), x1, x2)) -> c17(A__U11(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U11(0, x1, x2)) -> c17(A__U11(0, x1, x2), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c18_2, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2


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

(109) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(U11(0, x1, x2)) -> c17(A__U11(0, x1, x2), MARK(0))

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2), MARK(tt))
   MARK(U11(s(z0), x1, x2)) -> c17(A__U11(s(mark(z0)), x1, x2), MARK(s(z0)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2), MARK(tt))
   MARK(U11(s(z0), x1, x2)) -> c17(A__U11(s(mark(z0)), x1, x2), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c18_2, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2


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

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c18_2, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1


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

(113) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(U12(z0, z1, z2)) -> c18(A__U12(mark(z0), z1, z2), MARK(z0)) by 
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2), MARK(tt))
   MARK(U12(s(z0), x1, x2)) -> c18(A__U12(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U12(0, x1, x2)) -> c18(A__U12(0, x1, x2), MARK(0))

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
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   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2), MARK(tt))
   MARK(U12(s(z0), x1, x2)) -> c18(A__U12(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U12(0, x1, x2)) -> c18(A__U12(0, x1, x2), MARK(0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2), MARK(tt))
   MARK(U12(s(z0), x1, x2)) -> c18(A__U12(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U12(0, x1, x2)) -> c18(A__U12(0, x1, x2), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2


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

(115) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(U12(0, x1, x2)) -> c18(A__U12(0, x1, x2), MARK(0))

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2), MARK(tt))
   MARK(U12(s(z0), x1, x2)) -> c18(A__U12(s(mark(z0)), x1, x2), MARK(s(z0)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2), MARK(tt))
   MARK(U12(s(z0), x1, x2)) -> c18(A__U12(s(mark(z0)), x1, x2), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2


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

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c19_2, c20_2, c21_2, c22_2, c23_2, c24_2, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1


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

(119) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(plus(z0, z1)) -> c19(A__PLUS(mark(z0), mark(z1)), MARK(z0)) by 
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, tt)) -> c19(A__PLUS(mark(x0), tt), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c19(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c19(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1, z2), x1)) -> c19(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c19(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c19(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)), MARK(tt))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)), MARK(0))

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, tt)) -> c19(A__PLUS(mark(x0), tt), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c19(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c19(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1, z2), x1)) -> c19(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c19(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c19(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)), MARK(tt))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)), MARK(0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, tt)) -> c19(A__PLUS(mark(x0), tt), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c19(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c19(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1, z2), x1)) -> c19(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c19(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c19(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)), MARK(tt))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c20_2, c21_2, c22_2, c23_2, c24_2, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2


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

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

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c19(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c19(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1, z2), x1)) -> c19(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c19(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c19(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c19(MARK(x0))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
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   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
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   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
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   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
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   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
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   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
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   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
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   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
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   MARK(plus(plus(z0, z1), x1)) -> c19(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c19(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c19(MARK(x0))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c20_2, c21_2, c22_2, c23_2, c24_2, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1


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

(123) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(plus(z0, z1)) -> c20(A__PLUS(mark(z0), mark(z1)), MARK(z1)) by 
   MARK(plus(x0, U11(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c20(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, U22(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c20(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, tt)) -> c20(A__PLUS(mark(x0), tt), MARK(tt))
   MARK(plus(x0, s(z0))) -> c20(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0), MARK(0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c20(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1, z2), x1)) -> c20(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c20(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c20(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U22(z0, z1, z2), x1)) -> c20(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c20(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c19(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c19(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1, z2), x1)) -> c19(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c19(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c19(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c19(MARK(x0))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c20(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, U22(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c20(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, tt)) -> c20(A__PLUS(mark(x0), tt), MARK(tt))
   MARK(plus(x0, s(z0))) -> c20(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0), MARK(0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c20(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1, z2), x1)) -> c20(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c20(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c20(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U22(z0, z1, z2), x1)) -> c20(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c20(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
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   MARK(plus(U12(z0, z1, z2), x1)) -> c19(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c19(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c19(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c19(MARK(x0))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c20(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, U22(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c20(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, tt)) -> c20(A__PLUS(mark(x0), tt), MARK(tt))
   MARK(plus(x0, s(z0))) -> c20(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0), MARK(0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c20(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1, z2), x1)) -> c20(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c20(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c20(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U22(z0, z1, z2), x1)) -> c20(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c20(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c21_2, c22_2, c23_2, c24_2, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2


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

(125) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(plus(x0, tt)) -> c20(A__PLUS(mark(x0), tt), MARK(tt))

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c19(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c19(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1, z2), x1)) -> c19(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c19(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c19(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c19(MARK(x0))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c20(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, U22(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c20(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, s(z0))) -> c20(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0), MARK(0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c20(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1, z2), x1)) -> c20(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c20(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c20(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U22(z0, z1, z2), x1)) -> c20(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c20(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
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   MARK(plus(U12(z0, z1, z2), x1)) -> c19(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c19(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c19(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c19(MARK(x0))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c20(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, U22(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c20(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, s(z0))) -> c20(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0), MARK(0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c20(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1, z2), x1)) -> c20(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c20(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c20(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U22(z0, z1, z2), x1)) -> c20(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c20(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c21_2, c22_2, c23_2, c24_2, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2


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

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

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c19(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c19(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1, z2), x1)) -> c19(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c19(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c19(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c19(MARK(x0))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c20(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, U22(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c20(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, s(z0))) -> c20(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c20(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1, z2), x1)) -> c20(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c20(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c20(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U22(z0, z1, z2), x1)) -> c20(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c20(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c19(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c19(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1, z2), x1)) -> c19(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c19(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c19(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c19(MARK(x0))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c20(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, U22(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c20(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, s(z0))) -> c20(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c20(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1, z2), x1)) -> c20(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c20(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c20(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U22(z0, z1, z2), x1)) -> c20(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c20(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c21_2, c22_2, c23_2, c24_2, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1


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

(129) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(U21(z0, z1, z2)) -> c21(A__U21(mark(z0), z1, z2), MARK(z0)) by 
   MARK(U21(U11(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c21(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(U22(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c21(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(tt, x1, x2)) -> c21(A__U21(tt, x1, x2), MARK(tt))
   MARK(U21(s(z0), x1, x2)) -> c21(A__U21(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U21(0, x1, x2)) -> c21(A__U21(0, x1, x2), MARK(0))

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

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c19(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c19(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1, z2), x1)) -> c19(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c19(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c19(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c19(MARK(x0))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c20(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, U22(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c20(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, s(z0))) -> c20(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c20(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1, z2), x1)) -> c20(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c20(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c20(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U22(z0, z1, z2), x1)) -> c20(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c20(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0))
   MARK(U21(U11(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c21(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(U22(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c21(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(tt, x1, x2)) -> c21(A__U21(tt, x1, x2), MARK(tt))
   MARK(U21(s(z0), x1, x2)) -> c21(A__U21(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U21(0, x1, x2)) -> c21(A__U21(0, x1, x2), MARK(0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
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   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
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   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
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   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
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   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c19(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c19(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1, z2), x1)) -> c19(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c19(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c19(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c19(MARK(x0))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c20(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, U22(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c20(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, s(z0))) -> c20(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c20(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1, z2), x1)) -> c20(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c20(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c20(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U22(z0, z1, z2), x1)) -> c20(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c20(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0))
   MARK(U21(U11(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c21(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(U22(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c21(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(tt, x1, x2)) -> c21(A__U21(tt, x1, x2), MARK(tt))
   MARK(U21(s(z0), x1, x2)) -> c21(A__U21(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U21(0, x1, x2)) -> c21(A__U21(0, x1, x2), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c22_2, c23_2, c24_2, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2


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

(131) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(U21(0, x1, x2)) -> c21(A__U21(0, x1, x2), MARK(0))

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

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c19(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c19(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1, z2), x1)) -> c19(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c19(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c19(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c19(MARK(x0))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c20(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, U22(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c20(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, s(z0))) -> c20(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c20(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1, z2), x1)) -> c20(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c20(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c20(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U22(z0, z1, z2), x1)) -> c20(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c20(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0))
   MARK(U21(U11(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c21(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(U22(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c21(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(tt, x1, x2)) -> c21(A__U21(tt, x1, x2), MARK(tt))
   MARK(U21(s(z0), x1, x2)) -> c21(A__U21(s(mark(z0)), x1, x2), MARK(s(z0)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c19(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c19(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1, z2), x1)) -> c19(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c19(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c19(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c19(MARK(x0))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c20(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, U22(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c20(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, s(z0))) -> c20(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c20(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1, z2), x1)) -> c20(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c20(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c20(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U22(z0, z1, z2), x1)) -> c20(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c20(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0))
   MARK(U21(U11(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c21(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(U22(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c21(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(tt, x1, x2)) -> c21(A__U21(tt, x1, x2), MARK(tt))
   MARK(U21(s(z0), x1, x2)) -> c21(A__U21(s(mark(z0)), x1, x2), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c22_2, c23_2, c24_2, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2


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

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

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
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   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(U22(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c21(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(tt, x1, x2)) -> c21(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c21(MARK(s(z0)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c19(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c19(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1, z2), x1)) -> c19(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c19(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c19(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c19(MARK(x0))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c20(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, U22(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c20(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, s(z0))) -> c20(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c20(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1, z2), x1)) -> c20(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c20(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c20(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U22(z0, z1, z2), x1)) -> c20(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c20(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0))
   MARK(U21(U11(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c21(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(U22(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c21(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(tt, x1, x2)) -> c21(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c21(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c22_2, c23_2, c24_2, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1


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

(135) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(U22(z0, z1, z2)) -> c22(A__U22(mark(z0), z1, z2), MARK(z0)) by 
   MARK(U22(U11(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U22(U12(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U22(plus(z0, z1), x1, x2)) -> c22(A__U22(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U22(U21(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U22(U22(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U22(x(z0, z1), x1, x2)) -> c22(A__U22(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U22(tt, x1, x2)) -> c22(A__U22(tt, x1, x2), MARK(tt))
   MARK(U22(s(z0), x1, x2)) -> c22(A__U22(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U22(0, x1, x2)) -> c22(A__U22(0, x1, x2), MARK(0))

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

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
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   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
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   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
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   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
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   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
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   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
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   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
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   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c19(MARK(x0))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c20(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, U22(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c20(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, s(z0))) -> c20(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c20(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1, z2), x1)) -> c20(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c20(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c20(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U22(z0, z1, z2), x1)) -> c20(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c20(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0))
   MARK(U21(U11(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c21(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(U22(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c21(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(tt, x1, x2)) -> c21(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c21(MARK(s(z0)))
   MARK(U22(U11(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U22(U12(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U22(plus(z0, z1), x1, x2)) -> c22(A__U22(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U22(U21(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U22(U22(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U22(x(z0, z1), x1, x2)) -> c22(A__U22(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U22(tt, x1, x2)) -> c22(A__U22(tt, x1, x2), MARK(tt))
   MARK(U22(s(z0), x1, x2)) -> c22(A__U22(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U22(0, x1, x2)) -> c22(A__U22(0, x1, x2), MARK(0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c19(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c19(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1, z2), x1)) -> c19(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c19(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c19(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c19(MARK(x0))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c20(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, U22(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c20(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, s(z0))) -> c20(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c20(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1, z2), x1)) -> c20(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c20(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c20(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U22(z0, z1, z2), x1)) -> c20(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c20(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0))
   MARK(U21(U11(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c21(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(U22(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c21(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(tt, x1, x2)) -> c21(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c21(MARK(s(z0)))
   MARK(U22(U11(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U22(U12(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U22(plus(z0, z1), x1, x2)) -> c22(A__U22(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U22(U21(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U22(U22(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U22(x(z0, z1), x1, x2)) -> c22(A__U22(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U22(tt, x1, x2)) -> c22(A__U22(tt, x1, x2), MARK(tt))
   MARK(U22(s(z0), x1, x2)) -> c22(A__U22(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U22(0, x1, x2)) -> c22(A__U22(0, x1, x2), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c23_2, c24_2, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2


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

(137) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(U22(0, x1, x2)) -> c22(A__U22(0, x1, x2), MARK(0))

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

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c19(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c19(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1, z2), x1)) -> c19(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c19(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c19(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c19(MARK(x0))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c20(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, U22(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c20(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, s(z0))) -> c20(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c20(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1, z2), x1)) -> c20(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c20(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c20(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U22(z0, z1, z2), x1)) -> c20(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c20(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0))
   MARK(U21(U11(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c21(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(U22(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c21(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(tt, x1, x2)) -> c21(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c21(MARK(s(z0)))
   MARK(U22(U11(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U22(U12(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U22(plus(z0, z1), x1, x2)) -> c22(A__U22(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U22(U21(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U22(U22(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U22(x(z0, z1), x1, x2)) -> c22(A__U22(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U22(tt, x1, x2)) -> c22(A__U22(tt, x1, x2), MARK(tt))
   MARK(U22(s(z0), x1, x2)) -> c22(A__U22(s(mark(z0)), x1, x2), MARK(s(z0)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c19(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c19(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1, z2), x1)) -> c19(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c19(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c19(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c19(MARK(x0))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c20(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, U22(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c20(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, s(z0))) -> c20(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c20(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1, z2), x1)) -> c20(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c20(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c20(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U22(z0, z1, z2), x1)) -> c20(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c20(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0))
   MARK(U21(U11(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c21(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(U22(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c21(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(tt, x1, x2)) -> c21(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c21(MARK(s(z0)))
   MARK(U22(U11(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U22(U12(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U22(plus(z0, z1), x1, x2)) -> c22(A__U22(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U22(U21(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U22(U22(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U22(x(z0, z1), x1, x2)) -> c22(A__U22(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U22(tt, x1, x2)) -> c22(A__U22(tt, x1, x2), MARK(tt))
   MARK(U22(s(z0), x1, x2)) -> c22(A__U22(s(mark(z0)), x1, x2), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c23_2, c24_2, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2


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

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c19(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c19(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1, z2), x1)) -> c19(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c19(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c19(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c19(MARK(x0))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c20(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, U22(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c20(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, s(z0))) -> c20(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c20(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1, z2), x1)) -> c20(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c20(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c20(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U22(z0, z1, z2), x1)) -> c20(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c20(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0))
   MARK(U21(U11(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c21(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(U22(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c21(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(tt, x1, x2)) -> c21(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c21(MARK(s(z0)))
   MARK(U22(U11(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U22(U12(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U22(plus(z0, z1), x1, x2)) -> c22(A__U22(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U22(U21(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U22(U22(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U22(x(z0, z1), x1, x2)) -> c22(A__U22(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U22(tt, x1, x2)) -> c22(A__U22(tt, x1, x2))
   MARK(U22(s(z0), x1, x2)) -> c22(MARK(s(z0)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
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   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
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   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   MARK(plus(x0, U21(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, U22(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c20(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, s(z0))) -> c20(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c20(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1, z2), x1)) -> c20(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c20(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c20(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U22(z0, z1, z2), x1)) -> c20(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c20(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0))
   MARK(U21(U11(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c21(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(U22(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c21(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(tt, x1, x2)) -> c21(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c21(MARK(s(z0)))
   MARK(U22(U11(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U22(U12(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U22(plus(z0, z1), x1, x2)) -> c22(A__U22(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U22(U21(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U22(U22(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U22(x(z0, z1), x1, x2)) -> c22(A__U22(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U22(tt, x1, x2)) -> c22(A__U22(tt, x1, x2))
   MARK(U22(s(z0), x1, x2)) -> c22(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c23_2, c24_2, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1


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

(141) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(x(z0, z1)) -> c23(A__X(mark(z0), mark(z1)), MARK(z0)) by 
   MARK(x(x0, U11(z0, z1, z2))) -> c23(A__X(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U12(z0, z1, z2))) -> c23(A__X(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c23(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c23(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U22(z0, z1, z2))) -> c23(A__X(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c23(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, tt)) -> c23(A__X(mark(x0), tt), MARK(x0))
   MARK(x(x0, s(z0))) -> c23(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(x0, 0)) -> c23(A__X(mark(x0), 0), MARK(x0))
   MARK(x(U11(z0, z1, z2), x1)) -> c23(A__X(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(x(U12(z0, z1, z2), x1)) -> c23(A__X(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c23(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c23(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(U22(z0, z1, z2), x1)) -> c23(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c23(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(tt, x1)) -> c23(A__X(tt, mark(x1)), MARK(tt))
   MARK(x(s(z0), x1)) -> c23(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(0, x1)) -> c23(A__X(0, mark(x1)), MARK(0))

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

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
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   MARK(x(x0, U21(z0, z1, z2))) -> c23(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U22(z0, z1, z2))) -> c23(A__X(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c23(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, tt)) -> c23(A__X(mark(x0), tt), MARK(x0))
   MARK(x(x0, s(z0))) -> c23(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(x0, 0)) -> c23(A__X(mark(x0), 0), MARK(x0))
   MARK(x(U11(z0, z1, z2), x1)) -> c23(A__X(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(x(U12(z0, z1, z2), x1)) -> c23(A__X(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c23(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c23(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(U22(z0, z1, z2), x1)) -> c23(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c23(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(tt, x1)) -> c23(A__X(tt, mark(x1)), MARK(tt))
   MARK(x(s(z0), x1)) -> c23(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(0, x1)) -> c23(A__X(0, mark(x1)), MARK(0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c19(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c19(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1, z2), x1)) -> c19(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c19(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c19(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c19(MARK(x0))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c20(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, U22(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c20(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, s(z0))) -> c20(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c20(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1, z2), x1)) -> c20(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c20(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c20(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U22(z0, z1, z2), x1)) -> c20(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c20(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0))
   MARK(U21(U11(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c21(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(U22(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c21(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(tt, x1, x2)) -> c21(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c21(MARK(s(z0)))
   MARK(U22(U11(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U22(U12(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U22(plus(z0, z1), x1, x2)) -> c22(A__U22(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U22(U21(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U22(U22(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U22(x(z0, z1), x1, x2)) -> c22(A__U22(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U22(tt, x1, x2)) -> c22(A__U22(tt, x1, x2))
   MARK(U22(s(z0), x1, x2)) -> c22(MARK(s(z0)))
   MARK(x(x0, U11(z0, z1, z2))) -> c23(A__X(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U12(z0, z1, z2))) -> c23(A__X(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c23(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c23(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U22(z0, z1, z2))) -> c23(A__X(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c23(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, tt)) -> c23(A__X(mark(x0), tt), MARK(x0))
   MARK(x(x0, s(z0))) -> c23(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(x0, 0)) -> c23(A__X(mark(x0), 0), MARK(x0))
   MARK(x(U11(z0, z1, z2), x1)) -> c23(A__X(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(x(U12(z0, z1, z2), x1)) -> c23(A__X(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c23(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c23(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(U22(z0, z1, z2), x1)) -> c23(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c23(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(tt, x1)) -> c23(A__X(tt, mark(x1)), MARK(tt))
   MARK(x(s(z0), x1)) -> c23(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(0, x1)) -> c23(A__X(0, mark(x1)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c24_2, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2


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

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

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
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   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
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   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
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   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
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   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c19(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c19(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1, z2), x1)) -> c19(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c19(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c19(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c19(MARK(x0))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c20(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, U22(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c20(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, s(z0))) -> c20(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c20(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1, z2), x1)) -> c20(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c20(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c20(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U22(z0, z1, z2), x1)) -> c20(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c20(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0))
   MARK(U21(U11(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c21(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(U22(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c21(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(tt, x1, x2)) -> c21(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c21(MARK(s(z0)))
   MARK(U22(U11(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U22(U12(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U22(plus(z0, z1), x1, x2)) -> c22(A__U22(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U22(U21(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U22(U22(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U22(x(z0, z1), x1, x2)) -> c22(A__U22(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U22(tt, x1, x2)) -> c22(A__U22(tt, x1, x2))
   MARK(U22(s(z0), x1, x2)) -> c22(MARK(s(z0)))
   MARK(x(x0, U11(z0, z1, z2))) -> c23(A__X(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U12(z0, z1, z2))) -> c23(A__X(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c23(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c23(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U22(z0, z1, z2))) -> c23(A__X(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c23(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, s(z0))) -> c23(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(U11(z0, z1, z2), x1)) -> c23(A__X(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(x(U12(z0, z1, z2), x1)) -> c23(A__X(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c23(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c23(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(U22(z0, z1, z2), x1)) -> c23(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c23(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(s(z0), x1)) -> c23(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(x0, tt)) -> c23(MARK(x0))
   MARK(x(x0, 0)) -> c23(MARK(x0))
   MARK(x(tt, x1)) -> c23(A__X(tt, mark(x1)))
   MARK(x(0, x1)) -> c23(A__X(0, mark(x1)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
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   MARK(U22(U12(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U22(plus(z0, z1), x1, x2)) -> c22(A__U22(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U22(U21(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U22(U22(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U22(x(z0, z1), x1, x2)) -> c22(A__U22(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U22(tt, x1, x2)) -> c22(A__U22(tt, x1, x2))
   MARK(U22(s(z0), x1, x2)) -> c22(MARK(s(z0)))
   MARK(x(x0, U11(z0, z1, z2))) -> c23(A__X(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U12(z0, z1, z2))) -> c23(A__X(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c23(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c23(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U22(z0, z1, z2))) -> c23(A__X(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c23(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, s(z0))) -> c23(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(U11(z0, z1, z2), x1)) -> c23(A__X(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(x(U12(z0, z1, z2), x1)) -> c23(A__X(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c23(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c23(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(U22(z0, z1, z2), x1)) -> c23(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c23(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(s(z0), x1)) -> c23(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(x0, tt)) -> c23(MARK(x0))
   MARK(x(x0, 0)) -> c23(MARK(x0))
   MARK(x(tt, x1)) -> c23(A__X(tt, mark(x1)))
   MARK(x(0, x1)) -> c23(A__X(0, mark(x1)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c24_2, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1


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

(145) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(x(z0, z1)) -> c24(A__X(mark(z0), mark(z1)), MARK(z1)) by 
   MARK(x(x0, U11(z0, z1, z2))) -> c24(A__X(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(x(x0, U12(z0, z1, z2))) -> c24(A__X(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(x(x0, plus(z0, z1))) -> c24(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(x(x0, U21(z0, z1, z2))) -> c24(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(x(x0, U22(z0, z1, z2))) -> c24(A__X(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(x(x0, x(z0, z1))) -> c24(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(x(x0, tt)) -> c24(A__X(mark(x0), tt), MARK(tt))
   MARK(x(x0, s(z0))) -> c24(A__X(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(x(x0, 0)) -> c24(A__X(mark(x0), 0), MARK(0))
   MARK(x(U11(z0, z1, z2), x1)) -> c24(A__X(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(U12(z0, z1, z2), x1)) -> c24(A__X(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(plus(z0, z1), x1)) -> c24(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U21(z0, z1, z2), x1)) -> c24(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(U22(z0, z1, z2), x1)) -> c24(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c24(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c24(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c24(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c24(A__X(0, mark(x1)), MARK(x1))

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

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
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   MARK(x(plus(z0, z1), x1)) -> c23(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c23(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(U22(z0, z1, z2), x1)) -> c23(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c23(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(s(z0), x1)) -> c23(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(x0, tt)) -> c23(MARK(x0))
   MARK(x(x0, 0)) -> c23(MARK(x0))
   MARK(x(tt, x1)) -> c23(A__X(tt, mark(x1)))
   MARK(x(0, x1)) -> c23(A__X(0, mark(x1)))
   MARK(x(x0, U11(z0, z1, z2))) -> c24(A__X(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(x(x0, U12(z0, z1, z2))) -> c24(A__X(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(x(x0, plus(z0, z1))) -> c24(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(x(x0, U21(z0, z1, z2))) -> c24(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(x(x0, U22(z0, z1, z2))) -> c24(A__X(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(x(x0, x(z0, z1))) -> c24(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(x(x0, tt)) -> c24(A__X(mark(x0), tt), MARK(tt))
   MARK(x(x0, s(z0))) -> c24(A__X(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(x(x0, 0)) -> c24(A__X(mark(x0), 0), MARK(0))
   MARK(x(U11(z0, z1, z2), x1)) -> c24(A__X(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(U12(z0, z1, z2), x1)) -> c24(A__X(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(plus(z0, z1), x1)) -> c24(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U21(z0, z1, z2), x1)) -> c24(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(U22(z0, z1, z2), x1)) -> c24(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c24(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c24(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c24(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c24(A__X(0, mark(x1)), MARK(x1))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c19(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c19(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1, z2), x1)) -> c19(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c19(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c19(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c19(MARK(x0))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c20(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, U22(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c20(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, s(z0))) -> c20(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c20(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1, z2), x1)) -> c20(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c20(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c20(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U22(z0, z1, z2), x1)) -> c20(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c20(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0))
   MARK(U21(U11(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c21(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(U22(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c21(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(tt, x1, x2)) -> c21(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c21(MARK(s(z0)))
   MARK(U22(U11(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U22(U12(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U22(plus(z0, z1), x1, x2)) -> c22(A__U22(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U22(U21(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U22(U22(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U22(x(z0, z1), x1, x2)) -> c22(A__U22(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U22(tt, x1, x2)) -> c22(A__U22(tt, x1, x2))
   MARK(U22(s(z0), x1, x2)) -> c22(MARK(s(z0)))
   MARK(x(x0, U11(z0, z1, z2))) -> c23(A__X(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U12(z0, z1, z2))) -> c23(A__X(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c23(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c23(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U22(z0, z1, z2))) -> c23(A__X(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c23(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, s(z0))) -> c23(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(U11(z0, z1, z2), x1)) -> c23(A__X(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(x(U12(z0, z1, z2), x1)) -> c23(A__X(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c23(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c23(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(U22(z0, z1, z2), x1)) -> c23(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c23(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(s(z0), x1)) -> c23(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(x0, tt)) -> c23(MARK(x0))
   MARK(x(x0, 0)) -> c23(MARK(x0))
   MARK(x(tt, x1)) -> c23(A__X(tt, mark(x1)))
   MARK(x(0, x1)) -> c23(A__X(0, mark(x1)))
   MARK(x(x0, U11(z0, z1, z2))) -> c24(A__X(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(x(x0, U12(z0, z1, z2))) -> c24(A__X(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(x(x0, plus(z0, z1))) -> c24(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(x(x0, U21(z0, z1, z2))) -> c24(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(x(x0, U22(z0, z1, z2))) -> c24(A__X(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(x(x0, x(z0, z1))) -> c24(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(x(x0, tt)) -> c24(A__X(mark(x0), tt), MARK(tt))
   MARK(x(x0, s(z0))) -> c24(A__X(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(x(x0, 0)) -> c24(A__X(mark(x0), 0), MARK(0))
   MARK(x(U11(z0, z1, z2), x1)) -> c24(A__X(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(U12(z0, z1, z2), x1)) -> c24(A__X(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(plus(z0, z1), x1)) -> c24(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U21(z0, z1, z2), x1)) -> c24(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(U22(z0, z1, z2), x1)) -> c24(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c24(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c24(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c24(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c24(A__X(0, mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(147) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   MARK(x(x0, 0)) -> c24(A__X(mark(x0), 0), MARK(0))
   MARK(x(x0, tt)) -> c24(A__X(mark(x0), tt), MARK(tt))

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

(148)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c19(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c19(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1, z2), x1)) -> c19(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c19(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c19(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c19(MARK(x0))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c20(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, U22(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c20(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, s(z0))) -> c20(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c20(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1, z2), x1)) -> c20(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c20(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c20(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U22(z0, z1, z2), x1)) -> c20(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c20(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0))
   MARK(U21(U11(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c21(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(U22(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c21(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(tt, x1, x2)) -> c21(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c21(MARK(s(z0)))
   MARK(U22(U11(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U22(U12(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U22(plus(z0, z1), x1, x2)) -> c22(A__U22(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U22(U21(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U22(U22(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U22(x(z0, z1), x1, x2)) -> c22(A__U22(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U22(tt, x1, x2)) -> c22(A__U22(tt, x1, x2))
   MARK(U22(s(z0), x1, x2)) -> c22(MARK(s(z0)))
   MARK(x(x0, U11(z0, z1, z2))) -> c23(A__X(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U12(z0, z1, z2))) -> c23(A__X(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c23(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c23(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U22(z0, z1, z2))) -> c23(A__X(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c23(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, s(z0))) -> c23(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(U11(z0, z1, z2), x1)) -> c23(A__X(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(x(U12(z0, z1, z2), x1)) -> c23(A__X(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c23(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c23(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(U22(z0, z1, z2), x1)) -> c23(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c23(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(s(z0), x1)) -> c23(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(x0, tt)) -> c23(MARK(x0))
   MARK(x(x0, 0)) -> c23(MARK(x0))
   MARK(x(tt, x1)) -> c23(A__X(tt, mark(x1)))
   MARK(x(0, x1)) -> c23(A__X(0, mark(x1)))
   MARK(x(x0, U11(z0, z1, z2))) -> c24(A__X(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(x(x0, U12(z0, z1, z2))) -> c24(A__X(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(x(x0, plus(z0, z1))) -> c24(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(x(x0, U21(z0, z1, z2))) -> c24(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(x(x0, U22(z0, z1, z2))) -> c24(A__X(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(x(x0, x(z0, z1))) -> c24(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(x(x0, s(z0))) -> c24(A__X(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(x(U11(z0, z1, z2), x1)) -> c24(A__X(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(U12(z0, z1, z2), x1)) -> c24(A__X(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(plus(z0, z1), x1)) -> c24(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U21(z0, z1, z2), x1)) -> c24(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(U22(z0, z1, z2), x1)) -> c24(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c24(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c24(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c24(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c24(A__X(0, mark(x1)), MARK(x1))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
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   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
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   MARK(plus(U11(z0, z1, z2), x1)) -> c19(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1, z2), x1)) -> c19(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c19(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c19(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c19(MARK(x0))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c20(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, U22(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c20(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, s(z0))) -> c20(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c20(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1, z2), x1)) -> c20(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c20(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c20(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U22(z0, z1, z2), x1)) -> c20(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c20(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0))
   MARK(U21(U11(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c21(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(U22(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c21(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(tt, x1, x2)) -> c21(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c21(MARK(s(z0)))
   MARK(U22(U11(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U22(U12(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U22(plus(z0, z1), x1, x2)) -> c22(A__U22(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U22(U21(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U22(U22(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U22(x(z0, z1), x1, x2)) -> c22(A__U22(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U22(tt, x1, x2)) -> c22(A__U22(tt, x1, x2))
   MARK(U22(s(z0), x1, x2)) -> c22(MARK(s(z0)))
   MARK(x(x0, U11(z0, z1, z2))) -> c23(A__X(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U12(z0, z1, z2))) -> c23(A__X(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c23(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c23(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U22(z0, z1, z2))) -> c23(A__X(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c23(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, s(z0))) -> c23(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(U11(z0, z1, z2), x1)) -> c23(A__X(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(x(U12(z0, z1, z2), x1)) -> c23(A__X(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c23(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c23(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(U22(z0, z1, z2), x1)) -> c23(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c23(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(s(z0), x1)) -> c23(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(x0, tt)) -> c23(MARK(x0))
   MARK(x(x0, 0)) -> c23(MARK(x0))
   MARK(x(tt, x1)) -> c23(A__X(tt, mark(x1)))
   MARK(x(0, x1)) -> c23(A__X(0, mark(x1)))
   MARK(x(x0, U11(z0, z1, z2))) -> c24(A__X(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(x(x0, U12(z0, z1, z2))) -> c24(A__X(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(x(x0, plus(z0, z1))) -> c24(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(x(x0, U21(z0, z1, z2))) -> c24(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(x(x0, U22(z0, z1, z2))) -> c24(A__X(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(x(x0, x(z0, z1))) -> c24(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(x(x0, s(z0))) -> c24(A__X(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(x(U11(z0, z1, z2), x1)) -> c24(A__X(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(U12(z0, z1, z2), x1)) -> c24(A__X(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(plus(z0, z1), x1)) -> c24(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U21(z0, z1, z2), x1)) -> c24(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(U22(z0, z1, z2), x1)) -> c24(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c24(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c24(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c24(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c24(A__X(0, mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(149) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, U11(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(x1)) by 
   A__U12(tt, U11(x0, z1, z2), x3) -> c2(A__PLUS(mark(x3), U11(mark(x0), z1, z2)), MARK(x3))
   A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U11(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U11(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(tt))
   A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(0))

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

(150)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c19(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c19(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1, z2), x1)) -> c19(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c19(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c19(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c19(MARK(x0))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c20(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, U22(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c20(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, s(z0))) -> c20(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c20(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1, z2), x1)) -> c20(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c20(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c20(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U22(z0, z1, z2), x1)) -> c20(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c20(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0))
   MARK(U21(U11(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c21(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(U22(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c21(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(tt, x1, x2)) -> c21(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c21(MARK(s(z0)))
   MARK(U22(U11(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U22(U12(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U22(plus(z0, z1), x1, x2)) -> c22(A__U22(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U22(U21(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U22(U22(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U22(x(z0, z1), x1, x2)) -> c22(A__U22(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U22(tt, x1, x2)) -> c22(A__U22(tt, x1, x2))
   MARK(U22(s(z0), x1, x2)) -> c22(MARK(s(z0)))
   MARK(x(x0, U11(z0, z1, z2))) -> c23(A__X(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U12(z0, z1, z2))) -> c23(A__X(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c23(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c23(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U22(z0, z1, z2))) -> c23(A__X(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c23(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, s(z0))) -> c23(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(U11(z0, z1, z2), x1)) -> c23(A__X(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(x(U12(z0, z1, z2), x1)) -> c23(A__X(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c23(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c23(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(U22(z0, z1, z2), x1)) -> c23(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c23(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(s(z0), x1)) -> c23(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(x0, tt)) -> c23(MARK(x0))
   MARK(x(x0, 0)) -> c23(MARK(x0))
   MARK(x(tt, x1)) -> c23(A__X(tt, mark(x1)))
   MARK(x(0, x1)) -> c23(A__X(0, mark(x1)))
   MARK(x(x0, U11(z0, z1, z2))) -> c24(A__X(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(x(x0, U12(z0, z1, z2))) -> c24(A__X(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(x(x0, plus(z0, z1))) -> c24(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(x(x0, U21(z0, z1, z2))) -> c24(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(x(x0, U22(z0, z1, z2))) -> c24(A__X(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(x(x0, x(z0, z1))) -> c24(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(x(x0, s(z0))) -> c24(A__X(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(x(U11(z0, z1, z2), x1)) -> c24(A__X(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(U12(z0, z1, z2), x1)) -> c24(A__X(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(plus(z0, z1), x1)) -> c24(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U21(z0, z1, z2), x1)) -> c24(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(U22(z0, z1, z2), x1)) -> c24(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c24(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c24(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c24(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c24(A__X(0, mark(x1)), MARK(x1))
   A__U12(tt, U11(x0, z1, z2), x3) -> c2(A__PLUS(mark(x3), U11(mark(x0), z1, z2)), MARK(x3))
   A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U11(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U11(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(tt))
   A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
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   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
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   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
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   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
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   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
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   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
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   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
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   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
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   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c20(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, U22(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c20(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, s(z0))) -> c20(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c20(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1, z2), x1)) -> c20(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c20(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c20(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U22(z0, z1, z2), x1)) -> c20(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c20(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0))
   MARK(U21(U11(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c21(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(U22(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c21(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(tt, x1, x2)) -> c21(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c21(MARK(s(z0)))
   MARK(U22(U11(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U22(U12(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U22(plus(z0, z1), x1, x2)) -> c22(A__U22(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U22(U21(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U22(U22(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U22(x(z0, z1), x1, x2)) -> c22(A__U22(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U22(tt, x1, x2)) -> c22(A__U22(tt, x1, x2))
   MARK(U22(s(z0), x1, x2)) -> c22(MARK(s(z0)))
   MARK(x(x0, U11(z0, z1, z2))) -> c23(A__X(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U12(z0, z1, z2))) -> c23(A__X(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c23(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c23(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U22(z0, z1, z2))) -> c23(A__X(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c23(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, s(z0))) -> c23(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(U11(z0, z1, z2), x1)) -> c23(A__X(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(x(U12(z0, z1, z2), x1)) -> c23(A__X(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c23(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c23(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(U22(z0, z1, z2), x1)) -> c23(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c23(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(s(z0), x1)) -> c23(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(x0, tt)) -> c23(MARK(x0))
   MARK(x(x0, 0)) -> c23(MARK(x0))
   MARK(x(tt, x1)) -> c23(A__X(tt, mark(x1)))
   MARK(x(0, x1)) -> c23(A__X(0, mark(x1)))
   MARK(x(x0, U11(z0, z1, z2))) -> c24(A__X(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(x(x0, U12(z0, z1, z2))) -> c24(A__X(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(x(x0, plus(z0, z1))) -> c24(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(x(x0, U21(z0, z1, z2))) -> c24(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(x(x0, U22(z0, z1, z2))) -> c24(A__X(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(x(x0, x(z0, z1))) -> c24(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(x(x0, s(z0))) -> c24(A__X(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(x(U11(z0, z1, z2), x1)) -> c24(A__X(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(U12(z0, z1, z2), x1)) -> c24(A__X(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(plus(z0, z1), x1)) -> c24(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U21(z0, z1, z2), x1)) -> c24(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(U22(z0, z1, z2), x1)) -> c24(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c24(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c24(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c24(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c24(A__X(0, mark(x1)), MARK(x1))
   A__U12(tt, U11(x0, z1, z2), x3) -> c2(A__PLUS(mark(x3), U11(mark(x0), z1, z2)), MARK(x3))
   A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U11(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U11(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(tt))
   A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_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(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
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   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
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   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
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   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
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   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
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   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
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   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
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   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
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   MARK(plus(plus(z0, z1), x1)) -> c19(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c19(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c19(MARK(x0))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c20(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, U22(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c20(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, s(z0))) -> c20(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c20(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1, z2), x1)) -> c20(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c20(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c20(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U22(z0, z1, z2), x1)) -> c20(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c20(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0))
   MARK(U21(U11(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c21(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(U22(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c21(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(tt, x1, x2)) -> c21(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c21(MARK(s(z0)))
   MARK(U22(U11(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U22(U12(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U22(plus(z0, z1), x1, x2)) -> c22(A__U22(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U22(U21(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U22(U22(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U22(x(z0, z1), x1, x2)) -> c22(A__U22(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U22(tt, x1, x2)) -> c22(A__U22(tt, x1, x2))
   MARK(U22(s(z0), x1, x2)) -> c22(MARK(s(z0)))
   MARK(x(x0, U11(z0, z1, z2))) -> c23(A__X(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U12(z0, z1, z2))) -> c23(A__X(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c23(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c23(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U22(z0, z1, z2))) -> c23(A__X(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c23(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, s(z0))) -> c23(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(U11(z0, z1, z2), x1)) -> c23(A__X(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(x(U12(z0, z1, z2), x1)) -> c23(A__X(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c23(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c23(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(U22(z0, z1, z2), x1)) -> c23(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c23(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(s(z0), x1)) -> c23(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(x0, tt)) -> c23(MARK(x0))
   MARK(x(x0, 0)) -> c23(MARK(x0))
   MARK(x(tt, x1)) -> c23(A__X(tt, mark(x1)))
   MARK(x(0, x1)) -> c23(A__X(0, mark(x1)))
   MARK(x(x0, U11(z0, z1, z2))) -> c24(A__X(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(x(x0, U12(z0, z1, z2))) -> c24(A__X(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(x(x0, plus(z0, z1))) -> c24(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(x(x0, U21(z0, z1, z2))) -> c24(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(x(x0, U22(z0, z1, z2))) -> c24(A__X(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(x(x0, x(z0, z1))) -> c24(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(x(x0, s(z0))) -> c24(A__X(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(x(U11(z0, z1, z2), x1)) -> c24(A__X(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(U12(z0, z1, z2), x1)) -> c24(A__X(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(plus(z0, z1), x1)) -> c24(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U21(z0, z1, z2), x1)) -> c24(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(U22(z0, z1, z2), x1)) -> c24(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c24(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c24(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c24(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c24(A__X(0, mark(x1)), MARK(x1))
   A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U11(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U11(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
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   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
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   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
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   MARK(plus(x0, s(z0))) -> c20(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c20(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1, z2), x1)) -> c20(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c20(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c20(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U22(z0, z1, z2), x1)) -> c20(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c20(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0))
   MARK(U21(U11(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c21(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(U22(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c21(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(tt, x1, x2)) -> c21(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c21(MARK(s(z0)))
   MARK(U22(U11(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U22(U12(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U22(plus(z0, z1), x1, x2)) -> c22(A__U22(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U22(U21(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U22(U22(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U22(x(z0, z1), x1, x2)) -> c22(A__U22(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U22(tt, x1, x2)) -> c22(A__U22(tt, x1, x2))
   MARK(U22(s(z0), x1, x2)) -> c22(MARK(s(z0)))
   MARK(x(x0, U11(z0, z1, z2))) -> c23(A__X(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U12(z0, z1, z2))) -> c23(A__X(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c23(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c23(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U22(z0, z1, z2))) -> c23(A__X(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c23(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, s(z0))) -> c23(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(U11(z0, z1, z2), x1)) -> c23(A__X(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(x(U12(z0, z1, z2), x1)) -> c23(A__X(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c23(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c23(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(U22(z0, z1, z2), x1)) -> c23(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c23(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(s(z0), x1)) -> c23(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(x0, tt)) -> c23(MARK(x0))
   MARK(x(x0, 0)) -> c23(MARK(x0))
   MARK(x(tt, x1)) -> c23(A__X(tt, mark(x1)))
   MARK(x(0, x1)) -> c23(A__X(0, mark(x1)))
   MARK(x(x0, U11(z0, z1, z2))) -> c24(A__X(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(x(x0, U12(z0, z1, z2))) -> c24(A__X(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(x(x0, plus(z0, z1))) -> c24(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(x(x0, U21(z0, z1, z2))) -> c24(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(x(x0, U22(z0, z1, z2))) -> c24(A__X(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(x(x0, x(z0, z1))) -> c24(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(x(x0, s(z0))) -> c24(A__X(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(x(U11(z0, z1, z2), x1)) -> c24(A__X(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(U12(z0, z1, z2), x1)) -> c24(A__X(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(plus(z0, z1), x1)) -> c24(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U21(z0, z1, z2), x1)) -> c24(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(U22(z0, z1, z2), x1)) -> c24(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c24(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c24(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c24(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c24(A__X(0, mark(x1)), MARK(x1))
   A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U11(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U11(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(153) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, U12(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(x1)) by 
   A__U12(tt, U12(x0, z1, z2), x3) -> c2(A__PLUS(mark(x3), U12(mark(x0), z1, z2)), MARK(x3))
   A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U12(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3))
   A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3))
   A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U12(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(tt))
   A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(0))

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

(154)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
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   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
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   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
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   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c19(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c19(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1, z2), x1)) -> c19(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c19(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(U21(z0, z1, z2), x1)) -> c19(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(plus(U22(z0, z1, z2), x1)) -> c19(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(plus(x(z0, z1), x1)) -> c19(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c19(MARK(x0))
   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c19(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(plus(x0, U12(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c20(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, U21(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(plus(x0, U22(z0, z1, z2))) -> c20(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(plus(x0, x(z0, z1))) -> c20(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(plus(x0, s(z0))) -> c20(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1, z2), x1)) -> c20(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U12(z0, z1, z2), x1)) -> c20(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c20(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(U21(z0, z1, z2), x1)) -> c20(A__PLUS(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U22(z0, z1, z2), x1)) -> c20(A__PLUS(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(x(z0, z1), x1)) -> c20(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0))
   MARK(U21(U11(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c21(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(U22(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c21(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(tt, x1, x2)) -> c21(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c21(MARK(s(z0)))
   MARK(U22(U11(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U22(U12(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U22(plus(z0, z1), x1, x2)) -> c22(A__U22(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U22(U21(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U22(U22(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U22(x(z0, z1), x1, x2)) -> c22(A__U22(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U22(tt, x1, x2)) -> c22(A__U22(tt, x1, x2))
   MARK(U22(s(z0), x1, x2)) -> c22(MARK(s(z0)))
   MARK(x(x0, U11(z0, z1, z2))) -> c23(A__X(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U12(z0, z1, z2))) -> c23(A__X(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c23(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c23(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U22(z0, z1, z2))) -> c23(A__X(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c23(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, s(z0))) -> c23(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(U11(z0, z1, z2), x1)) -> c23(A__X(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(x(U12(z0, z1, z2), x1)) -> c23(A__X(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c23(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c23(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(U22(z0, z1, z2), x1)) -> c23(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c23(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(s(z0), x1)) -> c23(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(x0, tt)) -> c23(MARK(x0))
   MARK(x(x0, 0)) -> c23(MARK(x0))
   MARK(x(tt, x1)) -> c23(A__X(tt, mark(x1)))
   MARK(x(0, x1)) -> c23(A__X(0, mark(x1)))
   MARK(x(x0, U11(z0, z1, z2))) -> c24(A__X(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(x(x0, U12(z0, z1, z2))) -> c24(A__X(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(x(x0, plus(z0, z1))) -> c24(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(x(x0, U21(z0, z1, z2))) -> c24(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(x(x0, U22(z0, z1, z2))) -> c24(A__X(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(x(x0, x(z0, z1))) -> c24(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(x(x0, s(z0))) -> c24(A__X(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(x(U11(z0, z1, z2), x1)) -> c24(A__X(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(U12(z0, z1, z2), x1)) -> c24(A__X(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(plus(z0, z1), x1)) -> c24(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U21(z0, z1, z2), x1)) -> c24(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(U22(z0, z1, z2), x1)) -> c24(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c24(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c24(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c24(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c24(A__X(0, mark(x1)), MARK(x1))
   A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U11(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U11(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2)))
   A__U12(tt, U12(x0, z1, z2), x3) -> c2(A__PLUS(mark(x3), U12(mark(x0), z1, z2)), MARK(x3))
   A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U12(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3))
   A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3))
   A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U12(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(tt))
   A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
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   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
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   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_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(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
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   A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2)))
   A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U12(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3))
   A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3))
   A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U12(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2)))
   A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
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   A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U11(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2)))
   A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U12(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3))
   A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3))
   A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U12(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2)))
   A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(157) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, plus(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) by 
   A__U12(tt, plus(x0, x1), x2) -> c2(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(x2))
   A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, U22(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(U22(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(tt))
   A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(0))

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

(158)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
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   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0))
   MARK(U21(U11(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c21(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(U22(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c21(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(tt, x1, x2)) -> c21(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c21(MARK(s(z0)))
   MARK(U22(U11(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U22(U12(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U22(plus(z0, z1), x1, x2)) -> c22(A__U22(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U22(U21(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U22(U22(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U22(x(z0, z1), x1, x2)) -> c22(A__U22(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U22(tt, x1, x2)) -> c22(A__U22(tt, x1, x2))
   MARK(U22(s(z0), x1, x2)) -> c22(MARK(s(z0)))
   MARK(x(x0, U11(z0, z1, z2))) -> c23(A__X(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U12(z0, z1, z2))) -> c23(A__X(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c23(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c23(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U22(z0, z1, z2))) -> c23(A__X(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c23(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, s(z0))) -> c23(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(U11(z0, z1, z2), x1)) -> c23(A__X(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(x(U12(z0, z1, z2), x1)) -> c23(A__X(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c23(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c23(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(U22(z0, z1, z2), x1)) -> c23(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c23(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(s(z0), x1)) -> c23(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(x0, tt)) -> c23(MARK(x0))
   MARK(x(x0, 0)) -> c23(MARK(x0))
   MARK(x(tt, x1)) -> c23(A__X(tt, mark(x1)))
   MARK(x(0, x1)) -> c23(A__X(0, mark(x1)))
   MARK(x(x0, U11(z0, z1, z2))) -> c24(A__X(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(x(x0, U12(z0, z1, z2))) -> c24(A__X(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(x(x0, plus(z0, z1))) -> c24(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(x(x0, U21(z0, z1, z2))) -> c24(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(x(x0, U22(z0, z1, z2))) -> c24(A__X(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(x(x0, x(z0, z1))) -> c24(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(x(x0, s(z0))) -> c24(A__X(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(x(U11(z0, z1, z2), x1)) -> c24(A__X(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(U12(z0, z1, z2), x1)) -> c24(A__X(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(plus(z0, z1), x1)) -> c24(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U21(z0, z1, z2), x1)) -> c24(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(U22(z0, z1, z2), x1)) -> c24(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c24(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c24(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c24(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c24(A__X(0, mark(x1)), MARK(x1))
   A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U11(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U11(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2)))
   A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U12(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3))
   A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3))
   A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U12(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2)))
   A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2)))
   A__U12(tt, plus(x0, x1), x2) -> c2(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(x2))
   A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, U22(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(U22(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(tt))
   A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
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   A__U12(tt, tt, x1) -> c2(MARK(x1))
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   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
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   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
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   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
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   A__U12(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, U22(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(U22(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(tt))
   A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

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

(160)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
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   MARK(x(plus(z0, z1), x1)) -> c24(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U21(z0, z1, z2), x1)) -> c24(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(U22(z0, z1, z2), x1)) -> c24(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c24(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c24(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c24(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c24(A__X(0, mark(x1)), MARK(x1))
   A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U11(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U11(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2)))
   A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U12(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3))
   A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3))
   A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U12(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2)))
   A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2)))
   A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, U22(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(U22(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2))
   A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
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   MARK(plus(tt, x1)) -> c20(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c20(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c20(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c20(A__PLUS(mark(x0), 0))
   MARK(U21(U11(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U21(U12(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U21(plus(z0, z1), x1, x2)) -> c21(A__U21(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U21(U21(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U21(U22(z0, z1, z2), x1, x2)) -> c21(A__U21(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U21(x(z0, z1), x1, x2)) -> c21(A__U21(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U21(tt, x1, x2)) -> c21(A__U21(tt, x1, x2))
   MARK(U21(s(z0), x1, x2)) -> c21(MARK(s(z0)))
   MARK(U22(U11(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U22(U12(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U22(plus(z0, z1), x1, x2)) -> c22(A__U22(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U22(U21(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U22(U22(z0, z1, z2), x1, x2)) -> c22(A__U22(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U22(x(z0, z1), x1, x2)) -> c22(A__U22(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U22(tt, x1, x2)) -> c22(A__U22(tt, x1, x2))
   MARK(U22(s(z0), x1, x2)) -> c22(MARK(s(z0)))
   MARK(x(x0, U11(z0, z1, z2))) -> c23(A__X(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U12(z0, z1, z2))) -> c23(A__X(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, plus(z0, z1))) -> c23(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, U21(z0, z1, z2))) -> c23(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, U22(z0, z1, z2))) -> c23(A__X(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(x(x0, x(z0, z1))) -> c23(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(x(x0, s(z0))) -> c23(A__X(mark(x0), s(mark(z0))), MARK(x0))
   MARK(x(U11(z0, z1, z2), x1)) -> c23(A__X(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(x(U12(z0, z1, z2), x1)) -> c23(A__X(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
   MARK(x(plus(z0, z1), x1)) -> c23(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(x(U21(z0, z1, z2), x1)) -> c23(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(U21(z0, z1, z2)))
   MARK(x(U22(z0, z1, z2), x1)) -> c23(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(U22(z0, z1, z2)))
   MARK(x(x(z0, z1), x1)) -> c23(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1)))
   MARK(x(s(z0), x1)) -> c23(A__X(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(x(x0, tt)) -> c23(MARK(x0))
   MARK(x(x0, 0)) -> c23(MARK(x0))
   MARK(x(tt, x1)) -> c23(A__X(tt, mark(x1)))
   MARK(x(0, x1)) -> c23(A__X(0, mark(x1)))
   MARK(x(x0, U11(z0, z1, z2))) -> c24(A__X(mark(x0), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   MARK(x(x0, U12(z0, z1, z2))) -> c24(A__X(mark(x0), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   MARK(x(x0, plus(z0, z1))) -> c24(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(x(x0, U21(z0, z1, z2))) -> c24(A__X(mark(x0), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   MARK(x(x0, U22(z0, z1, z2))) -> c24(A__X(mark(x0), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   MARK(x(x0, x(z0, z1))) -> c24(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   MARK(x(x0, s(z0))) -> c24(A__X(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(x(U11(z0, z1, z2), x1)) -> c24(A__X(a__U11(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(U12(z0, z1, z2), x1)) -> c24(A__X(a__U12(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(plus(z0, z1), x1)) -> c24(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(U21(z0, z1, z2), x1)) -> c24(A__X(a__U21(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(U22(z0, z1, z2), x1)) -> c24(A__X(a__U22(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(x(x(z0, z1), x1)) -> c24(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(x(tt, x1)) -> c24(A__X(tt, mark(x1)), MARK(x1))
   MARK(x(s(z0), x1)) -> c24(A__X(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(x(0, x1)) -> c24(A__X(0, mark(x1)), MARK(x1))
   A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U11(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U11(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2)))
   A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U12(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3))
   A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3))
   A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U12(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2)))
   A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2)))
   A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, U22(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(U22(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2))
   A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(161) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, U21(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(x1)) by 
   A__U12(tt, U21(x0, z1, z2), x3) -> c2(A__PLUS(mark(x3), U21(mark(x0), z1, z2)), MARK(x3))
   A__U12(tt, U21(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3))
   A__U12(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3))
   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(tt))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(0))

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

(162)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
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   A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U11(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2)))
   A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U12(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3))
   A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3))
   A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U12(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2)))
   A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2)))
   A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, U22(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(U22(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2))
   A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U12(tt, U21(x0, z1, z2), x3) -> c2(A__PLUS(mark(x3), U21(mark(x0), z1, z2)), MARK(x3))
   A__U12(tt, U21(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3))
   A__U12(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3))
   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(tt))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
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   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
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   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
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   A__U12(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3))
   A__U12(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3))
   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(tt))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

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

(164)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
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   A__U12(tt, U11(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U11(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U11(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(x3))
   A__U12(tt, U11(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U11(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(x3))
   A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U11(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U11(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U11(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U11(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U11(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U11(mark(x0), x1, x2)))
   A__U12(tt, U11(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U11(mark(x0), x1, x2)))
   A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U12(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3))
   A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3))
   A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U12(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2)))
   A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2)))
   A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, U22(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(U22(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2))
   A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U12(tt, U21(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3))
   A__U12(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3))
   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
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   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
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   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
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   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
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   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
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   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
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   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
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   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
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   A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U12(tt, U21(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3))
   A__U12(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3))
   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(165) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, U22(z0, z1, z2), x1) -> c2(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(x1)) by 
   A__U12(tt, U22(x0, z1, z2), x3) -> c2(A__PLUS(mark(x3), U22(mark(x0), z1, z2)), MARK(x3))
   A__U12(tt, U22(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U22(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U22(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(x3))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U22(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(0, x1, x2)), MARK(x3))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U22(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U22(mark(x0), x1, x2)), MARK(tt))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U22(mark(x0), x1, x2)), MARK(0))

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

(166)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
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   A__U12(tt, U22(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U22(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(0, x1, x2)), MARK(x3))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U22(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U22(mark(x0), x1, x2)), MARK(tt))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U22(mark(x0), x1, x2)), MARK(0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
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   A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U12(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3))
   A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3))
   A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U12(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2)))
   A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2)))
   A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, U22(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(U22(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2))
   A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U12(tt, U21(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3))
   A__U12(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3))
   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c2(A__PLUS(mark(x3), U22(mark(x0), z1, z2)), MARK(x3))
   A__U12(tt, U22(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U22(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U22(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(x3))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U22(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(0, x1, x2)), MARK(x3))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U22(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U22(mark(x0), x1, x2)), MARK(tt))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U22(mark(x0), x1, x2)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

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

(168)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
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   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
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   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
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   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
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   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
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   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
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   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
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   A__U12(tt, plus(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2))
   A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U12(tt, U21(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3))
   A__U12(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3))
   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)))
   A__U12(tt, U22(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U22(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U22(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(x3))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U22(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(0, x1, x2)), MARK(x3))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U22(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U22(mark(x0), x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U22(mark(x0), x1, x2)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
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   A__U12(tt, U22(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(0, x1, x2)), MARK(x3))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U22(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U22(mark(x0), x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U22(mark(x0), x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(169) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, x(z0, z1), x1) -> c2(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) by 
   A__U12(tt, x(x0, x1), x2) -> c2(A__PLUS(mark(x2), x(mark(x0), mark(x1))), MARK(x2))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, x(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x2))
   A__U12(tt, x(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x2))
   A__U12(tt, x(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x2))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U12(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U12(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U12(z0, z1, z2)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(tt))
   A__U12(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(0))

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

(170)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
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   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U22(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U22(mark(x0), x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U22(mark(x0), x1, x2)))
   A__U12(tt, x(x0, x1), x2) -> c2(A__PLUS(mark(x2), x(mark(x0), mark(x1))), MARK(x2))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, x(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x2))
   A__U12(tt, x(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x2))
   A__U12(tt, x(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x2))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U12(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U12(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U12(z0, z1, z2)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(tt))
   A__U12(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
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   A__U12(tt, x(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x2))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U12(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U12(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U12(z0, z1, z2)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(tt))
   A__U12(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

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

(172)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
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   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U12(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U12(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U12(z0, z1, z2)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U12(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U12(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
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   A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U12(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U12(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U12(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(x3))
   A__U12(tt, U12(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U12(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(x3))
   A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U12(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U12(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U12(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U12(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U12(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U12(mark(x0), x1, x2)))
   A__U12(tt, U12(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U12(mark(x0), x1, x2)))
   A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, plus(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, U22(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, plus(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, plus(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U12(tt, plus(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U12(tt, plus(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, plus(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(U22(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, plus(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2))
   A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U12(tt, U21(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3))
   A__U12(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3))
   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)))
   A__U12(tt, U22(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U22(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U22(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(x3))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U22(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(0, x1, x2)), MARK(x3))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U22(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U22(mark(x0), x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U22(mark(x0), x1, x2)))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, x(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x2))
   A__U12(tt, x(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x2))
   A__U12(tt, x(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x2))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U12(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U12(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U12(z0, z1, z2)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U12(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U12(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(173) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, x0, U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(U11(z0, z1, z2))) by 
   A__U12(tt, U11(z0, z1, z2), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), a__U11(mark(z0), z1, z2)), MARK(U11(x1, x2, x3)))
   A__U12(tt, U12(z0, z1, z2), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), a__U12(mark(z0), z1, z2)), MARK(U11(x1, x2, x3)))
   A__U12(tt, plus(z0, z1), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), a__plus(mark(z0), mark(z1))), MARK(U11(x1, x2, x3)))
   A__U12(tt, U21(z0, z1, z2), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), a__U21(mark(z0), z1, z2)), MARK(U11(x1, x2, x3)))
   A__U12(tt, U22(z0, z1, z2), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), a__U22(mark(z0), z1, z2)), MARK(U11(x1, x2, x3)))
   A__U12(tt, x(z0, z1), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), a__x(mark(z0), mark(z1))), MARK(U11(x1, x2, x3)))
   A__U12(tt, tt, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), tt), MARK(U11(x1, x2, x3)))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(U11(0, x2, x3)))

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

(174)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
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   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U12(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U12(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U12(z0, z1, z2)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U12(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U12(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
   A__U12(tt, tt, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), tt), MARK(U11(x1, x2, x3)))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(U11(0, x2, x3)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
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   A__U12(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U12(z0, z1, z2)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U12(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U12(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
   A__U12(tt, tt, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), tt), MARK(U11(x1, x2, x3)))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U12(tt, x0, U11(0, x2, x3)) -> c2(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_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

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

(176)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
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   A__U12(tt, x(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x2))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U12(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U12(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U12(z0, z1, z2)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U12(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U12(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
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   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U12(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U12(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U12(z0, z1, z2)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U12(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U12(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(177) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, x0, U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(U12(z0, z1, z2))) by 
   A__U12(tt, U11(z0, z1, z2), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), a__U11(mark(z0), z1, z2)), MARK(U12(x1, x2, x3)))
   A__U12(tt, U12(z0, z1, z2), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), a__U12(mark(z0), z1, z2)), MARK(U12(x1, x2, x3)))
   A__U12(tt, plus(z0, z1), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), a__plus(mark(z0), mark(z1))), MARK(U12(x1, x2, x3)))
   A__U12(tt, U21(z0, z1, z2), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), a__U21(mark(z0), z1, z2)), MARK(U12(x1, x2, x3)))
   A__U12(tt, U22(z0, z1, z2), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), a__U22(mark(z0), z1, z2)), MARK(U12(x1, x2, x3)))
   A__U12(tt, x(z0, z1), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), a__x(mark(z0), mark(z1))), MARK(U12(x1, x2, x3)))
   A__U12(tt, tt, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), tt), MARK(U12(x1, x2, x3)))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3)))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2)))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3)))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3)))
   A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(U12(0, x2, x3)))

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

(178)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
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   A__U12(tt, U22(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U22(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U22(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(x3))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U22(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(0, x1, x2)), MARK(x3))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U22(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U22(mark(x0), x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U22(mark(x0), x1, x2)))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, x(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x2))
   A__U12(tt, x(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x2))
   A__U12(tt, x(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x2))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U12(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U12(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U12(z0, z1, z2)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U12(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U12(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0)))
   A__U12(tt, tt, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), tt), MARK(U12(x1, x2, x3)))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3)))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2)))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3)))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3)))
   A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(U12(0, x2, x3)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
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   A__U12(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3))
   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)))
   A__U12(tt, U22(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U22(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U22(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(x3))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U22(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(0, x1, x2)), MARK(x3))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U22(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U22(mark(x0), x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U22(mark(x0), x1, x2)))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, x(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x2))
   A__U12(tt, x(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x2))
   A__U12(tt, x(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x2))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U12(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U12(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U12(z0, z1, z2)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U12(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U12(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0)))
   A__U12(tt, tt, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), tt), MARK(U12(x1, x2, x3)))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3)))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2)))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3)))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3)))
   A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(U12(0, x2, x3)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_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(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
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   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
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   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
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   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
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   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
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   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
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   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
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   A__U12(tt, plus(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, plus(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U12(tt, plus(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U12(tt, plus(0, x1), x2) -> c2(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, plus(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, plus(x0, x1), x2) -> c2(MARK(x2))
   A__U12(tt, plus(x0, x1), tt) -> c2(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U12(tt, plus(x0, x1), 0) -> c2(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U12(tt, U21(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U21(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U21(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(x3))
   A__U12(tt, U21(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U21(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(x3))
   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)))
   A__U12(tt, U22(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U22(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U22(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(x3))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U22(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(0, x1, x2)), MARK(x3))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U22(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U22(mark(x0), x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U22(mark(x0), x1, x2)))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, x(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x2))
   A__U12(tt, x(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x2))
   A__U12(tt, x(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x2))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U12(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U12(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U12(z0, z1, z2)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U12(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U12(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3)))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2)))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3)))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3)))
   A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
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   A__U12(tt, tt, x1) -> c2(MARK(x1))
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   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
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   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
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   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
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   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3)))
   A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(181) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, x0, plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) by 
   A__U12(tt, U11(z0, z1, z2), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), a__U11(mark(z0), z1, z2)), MARK(plus(x1, x2)))
   A__U12(tt, U12(z0, z1, z2), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), a__U12(mark(z0), z1, z2)), MARK(plus(x1, x2)))
   A__U12(tt, plus(z0, z1), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), a__plus(mark(z0), mark(z1))), MARK(plus(x1, x2)))
   A__U12(tt, U21(z0, z1, z2), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), a__U21(mark(z0), z1, z2)), MARK(plus(x1, x2)))
   A__U12(tt, U22(z0, z1, z2), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), a__U22(mark(z0), z1, z2)), MARK(plus(x1, x2)))
   A__U12(tt, x(z0, z1), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), a__x(mark(z0), mark(z1))), MARK(plus(x1, x2)))
   A__U12(tt, tt, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(plus(x1, x2)))
   A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))

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

(182)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
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   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, x(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x2))
   A__U12(tt, x(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x2))
   A__U12(tt, x(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x2))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U12(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U12(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U12(z0, z1, z2)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U12(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U12(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3)))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2)))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3)))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3)))
   A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0)))
   A__U12(tt, tt, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(plus(x1, x2)))
   A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
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   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
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   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U21(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U21(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U21(mark(x0), x1, x2)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U21(mark(x0), x1, x2)))
   A__U12(tt, U22(U11(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U11(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(U12(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U12(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(plus(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U22(U21(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U21(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(U22(z0, z1, z2), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__U22(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U12(tt, U22(x(z0, z1), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U12(tt, U22(tt, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(x3))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(x3))
   A__U12(tt, U22(0, x1, x2), x3) -> c2(A__PLUS(mark(x3), a__U22(0, x1, x2)), MARK(x3))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(x(z0, z1)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(s(z0)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c2(MARK(x3))
   A__U12(tt, U22(x0, x1, x2), tt) -> c2(A__PLUS(tt, a__U22(mark(x0), x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U22(mark(x0), x1, x2)))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, x(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x2))
   A__U12(tt, x(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x2))
   A__U12(tt, x(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x2))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U12(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U12(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U12(z0, z1, z2)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U12(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U12(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3)))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2)))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3)))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3)))
   A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0)))
   A__U12(tt, tt, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(plus(x1, x2)))
   A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_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(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
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   A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3)))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2)))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3)))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3)))
   A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
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   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U12(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U12(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U12(z0, z1, z2)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U12(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U12(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3)))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2)))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3)))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3)))
   A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(185) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, x0, U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(U21(z0, z1, z2))) by 
   A__U12(tt, U11(z0, z1, z2), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), a__U11(mark(z0), z1, z2)), MARK(U21(x1, x2, x3)))
   A__U12(tt, U12(z0, z1, z2), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), a__U12(mark(z0), z1, z2)), MARK(U21(x1, x2, x3)))
   A__U12(tt, plus(z0, z1), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), a__plus(mark(z0), mark(z1))), MARK(U21(x1, x2, x3)))
   A__U12(tt, U21(z0, z1, z2), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), a__U21(mark(z0), z1, z2)), MARK(U21(x1, x2, x3)))
   A__U12(tt, U22(z0, z1, z2), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), a__U22(mark(z0), z1, z2)), MARK(U21(x1, x2, x3)))
   A__U12(tt, x(z0, z1), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), a__x(mark(z0), mark(z1))), MARK(U21(x1, x2, x3)))
   A__U12(tt, tt, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), tt), MARK(U21(x1, x2, x3)))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U12(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(U21(0, x2, x3)))

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

(186)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
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   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
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   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
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   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
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   A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U12(tt, tt, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), tt), MARK(U21(x1, x2, x3)))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U12(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(U21(0, x2, x3)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
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   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U12(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U12(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U12(z0, z1, z2)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U12(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U12(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3)))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2)))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3)))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3)))
   A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U12(tt, tt, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), tt), MARK(U21(x1, x2, x3)))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U12(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(U21(0, x2, x3)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_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(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
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   A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U12(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
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   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U12(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U12(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3)))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2)))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3)))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3)))
   A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U12(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(189) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, x0, U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(U22(z0, z1, z2))) by 
   A__U12(tt, U11(z0, z1, z2), U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), a__U11(mark(z0), z1, z2)), MARK(U22(x1, x2, x3)))
   A__U12(tt, U12(z0, z1, z2), U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), a__U12(mark(z0), z1, z2)), MARK(U22(x1, x2, x3)))
   A__U12(tt, plus(z0, z1), U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), a__plus(mark(z0), mark(z1))), MARK(U22(x1, x2, x3)))
   A__U12(tt, U21(z0, z1, z2), U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), a__U21(mark(z0), z1, z2)), MARK(U22(x1, x2, x3)))
   A__U12(tt, U22(z0, z1, z2), U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), a__U22(mark(z0), z1, z2)), MARK(U22(x1, x2, x3)))
   A__U12(tt, x(z0, z1), U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), a__x(mark(z0), mark(z1))), MARK(U22(x1, x2, x3)))
   A__U12(tt, tt, U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), tt), MARK(U22(x1, x2, x3)))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(U22(x1, x2, x3)))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), 0), MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c2(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(U22(x1, z1, z2)))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c2(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(U22(tt, x2, x3)))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c2(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(U22(s(z0), x2, x3)))
   A__U12(tt, x0, U22(0, x2, x3)) -> c2(A__PLUS(a__U22(0, x2, x3), mark(x0)), MARK(U22(0, x2, x3)))

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

(190)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
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   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
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   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
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   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
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   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
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   A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U12(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U12(tt, tt, U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), tt), MARK(U22(x1, x2, x3)))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(U22(x1, x2, x3)))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), 0), MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c2(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(U22(x1, z1, z2)))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c2(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(U22(tt, x2, x3)))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c2(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(U22(s(z0), x2, x3)))
   A__U12(tt, x0, U22(0, x2, x3)) -> c2(A__PLUS(a__U22(0, x2, x3), mark(x0)), MARK(U22(0, x2, x3)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
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   A__U12(tt, U22(x0, x1, x2), 0) -> c2(A__PLUS(0, a__U22(mark(x0), x1, x2)))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x2))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x2))
   A__U12(tt, x(x0, tt), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x2))
   A__U12(tt, x(x0, s(z0)), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x2))
   A__U12(tt, x(x0, 0), x2) -> c2(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x2))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c2(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U12(tt, x(tt, x1), x2) -> c2(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x2))
   A__U12(tt, x(s(z0), x1), x2) -> c2(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x2))
   A__U12(tt, x(0, x1), x2) -> c2(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x2))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c2(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U11(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c2(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U12(z0, z1, z2)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c2(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c2(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U21(z0, z1, z2)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c2(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(z0, z1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c2(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(s(z0)))
   A__U12(tt, x(x0, x1), x2) -> c2(MARK(x2))
   A__U12(tt, x(x0, x1), tt) -> c2(A__PLUS(tt, a__x(mark(x0), mark(x1))))
   A__U12(tt, x(x0, x1), 0) -> c2(A__PLUS(0, a__x(mark(x0), mark(x1))))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(U11(x1, x2, x3)))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c2(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c2(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(U11(x1, z1, z2)))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3)))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2)))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3)))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3)))
   A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U12(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U12(tt, tt, U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), tt), MARK(U22(x1, x2, x3)))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(U22(x1, x2, x3)))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), 0), MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c2(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(U22(x1, z1, z2)))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c2(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(U22(tt, x2, x3)))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c2(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(U22(s(z0), x2, x3)))
   A__U12(tt, x0, U22(0, x2, x3)) -> c2(A__PLUS(a__U22(0, x2, x3), mark(x0)), MARK(U22(0, x2, x3)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_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(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
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   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3)))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2)))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3)))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3)))
   A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U12(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(U22(x1, x2, x3)))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), 0), MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c2(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(U22(x1, z1, z2)))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c2(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(U22(tt, x2, x3)))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c2(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(U22(s(z0), x2, x3)))
   A__U12(tt, tt, U22(x1, x2, x3)) -> c2(MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(0, x2, x3)) -> c2(A__PLUS(a__U22(0, x2, x3), mark(x0)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1)))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
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   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c2(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(U22(tt, x2, x3)))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c2(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(U22(s(z0), x2, x3)))
   A__U12(tt, tt, U22(x1, x2, x3)) -> c2(MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(0, x2, x3)) -> c2(A__PLUS(a__U22(0, x2, x3), mark(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(193) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, x0, x(z0, z1)) -> c2(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) by 
   A__U12(tt, U11(z0, z1, z2), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), a__U11(mark(z0), z1, z2)), MARK(x(x1, x2)))
   A__U12(tt, U12(z0, z1, z2), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), a__U12(mark(z0), z1, z2)), MARK(x(x1, x2)))
   A__U12(tt, plus(z0, z1), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), a__plus(mark(z0), mark(z1))), MARK(x(x1, x2)))
   A__U12(tt, U21(z0, z1, z2), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), a__U21(mark(z0), z1, z2)), MARK(x(x1, x2)))
   A__U12(tt, U22(z0, z1, z2), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), a__U22(mark(z0), z1, z2)), MARK(x(x1, x2)))
   A__U12(tt, x(z0, z1), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), a__x(mark(z0), mark(z1))), MARK(x(x1, x2)))
   A__U12(tt, tt, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), tt), MARK(x(x1, x2)))
   A__U12(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U12(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U12(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U12(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U12(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U12(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U12(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U12(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U12(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))

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

(194)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
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   A__U12(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U12(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U12(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U12(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U12(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U12(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U12(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
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   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3)))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2)))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3)))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3)))
   A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U12(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(U22(x1, x2, x3)))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), 0), MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c2(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(U22(x1, z1, z2)))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c2(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(U22(tt, x2, x3)))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c2(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(U22(s(z0), x2, x3)))
   A__U12(tt, tt, U22(x1, x2, x3)) -> c2(MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(0, x2, x3)) -> c2(A__PLUS(a__U22(0, x2, x3), mark(x0)))
   A__U12(tt, tt, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), tt), MARK(x(x1, x2)))
   A__U12(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U12(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U12(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U12(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U12(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U12(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U12(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U12(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U12(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_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(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
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   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
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   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
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   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
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   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
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   A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U12(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(U22(x1, x2, x3)))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), 0), MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c2(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(U22(x1, z1, z2)))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c2(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(U22(tt, x2, x3)))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c2(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(U22(s(z0), x2, x3)))
   A__U12(tt, tt, U22(x1, x2, x3)) -> c2(MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(0, x2, x3)) -> c2(A__PLUS(a__U22(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U12(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U12(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U12(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U12(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U12(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U12(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U12(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U12(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U12(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
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   A__U12(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U12(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(U22(x1, x2, x3)))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), 0), MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c2(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(U22(x1, z1, z2)))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c2(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(U22(tt, x2, x3)))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c2(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(U22(s(z0), x2, x3)))
   A__U12(tt, tt, U22(x1, x2, x3)) -> c2(MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(0, x2, x3)) -> c2(A__PLUS(a__U22(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U12(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U12(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U12(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U12(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U12(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U12(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U12(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U12(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U12(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(197) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, x0, s(z0)) -> c2(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) by 
   A__U12(tt, U11(z0, z1, z2), s(x1)) -> c2(A__PLUS(s(mark(x1)), a__U11(mark(z0), z1, z2)), MARK(s(x1)))
   A__U12(tt, U12(z0, z1, z2), s(x1)) -> c2(A__PLUS(s(mark(x1)), a__U12(mark(z0), z1, z2)), MARK(s(x1)))
   A__U12(tt, plus(z0, z1), s(x1)) -> c2(A__PLUS(s(mark(x1)), a__plus(mark(z0), mark(z1))), MARK(s(x1)))
   A__U12(tt, U21(z0, z1, z2), s(x1)) -> c2(A__PLUS(s(mark(x1)), a__U21(mark(z0), z1, z2)), MARK(s(x1)))
   A__U12(tt, U22(z0, z1, z2), s(x1)) -> c2(A__PLUS(s(mark(x1)), a__U22(mark(z0), z1, z2)), MARK(s(x1)))
   A__U12(tt, x(z0, z1), s(x1)) -> c2(A__PLUS(s(mark(x1)), a__x(mark(z0), mark(z1))), MARK(s(x1)))
   A__U12(tt, tt, s(x1)) -> c2(A__PLUS(s(mark(x1)), tt), MARK(s(x1)))
   A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2))))
   A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2))))
   A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U12(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U12(tt, x0, s(U22(z0, z1, z2))) -> c2(A__PLUS(s(a__U22(mark(z0), z1, z2)), mark(x0)), MARK(s(U22(z0, z1, z2))))
   A__U12(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1)))

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

(198)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
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   A__U12(tt, 0, U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), 0), MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c2(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(U22(x1, z1, z2)))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c2(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(U22(tt, x2, x3)))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c2(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(U22(s(z0), x2, x3)))
   A__U12(tt, tt, U22(x1, x2, x3)) -> c2(MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(0, x2, x3)) -> c2(A__PLUS(a__U22(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U12(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U12(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U12(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U12(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U12(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U12(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U12(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U12(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U12(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U12(tt, tt, s(x1)) -> c2(A__PLUS(s(mark(x1)), tt), MARK(s(x1)))
   A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2))))
   A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2))))
   A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U12(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U12(tt, x0, s(U22(z0, z1, z2))) -> c2(A__PLUS(s(a__U22(mark(z0), z1, z2)), mark(x0)), MARK(s(U22(z0, z1, z2))))
   A__U12(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
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   A__U12(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U12(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U12(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U12(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U12(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U12(tt, tt, s(x1)) -> c2(A__PLUS(s(mark(x1)), tt), MARK(s(x1)))
   A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2))))
   A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2))))
   A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U12(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U12(tt, x0, s(U22(z0, z1, z2))) -> c2(A__PLUS(s(a__U22(mark(z0), z1, z2)), mark(x0)), MARK(s(U22(z0, z1, z2))))
   A__U12(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

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

(200)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
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   A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2))))
   A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2))))
   A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U12(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U12(tt, x0, s(U22(z0, z1, z2))) -> c2(A__PLUS(s(a__U22(mark(z0), z1, z2)), mark(x0)), MARK(s(U22(z0, z1, z2))))
   A__U12(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0)))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
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   A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3)))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2)))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3)))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3)))
   A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U12(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(U22(x1, x2, x3)))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), 0), MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c2(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(U22(x1, z1, z2)))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c2(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(U22(tt, x2, x3)))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c2(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(U22(s(z0), x2, x3)))
   A__U12(tt, tt, U22(x1, x2, x3)) -> c2(MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(0, x2, x3)) -> c2(A__PLUS(a__U22(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U12(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U12(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U12(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U12(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U12(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U12(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U12(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U12(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U12(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2))))
   A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2))))
   A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U12(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U12(tt, x0, s(U22(z0, z1, z2))) -> c2(A__PLUS(s(a__U22(mark(z0), z1, z2)), mark(x0)), MARK(s(U22(z0, z1, z2))))
   A__U12(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(201) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, x0, tt) -> c2(A__PLUS(tt, mark(x0))) by 
   A__U12(tt, U11(z0, z1, z2), tt) -> c2(A__PLUS(tt, a__U11(mark(z0), z1, z2)))
   A__U12(tt, U12(z0, z1, z2), tt) -> c2(A__PLUS(tt, a__U12(mark(z0), z1, z2)))
   A__U12(tt, plus(z0, z1), tt) -> c2(A__PLUS(tt, a__plus(mark(z0), mark(z1))))
   A__U12(tt, U21(z0, z1, z2), tt) -> c2(A__PLUS(tt, a__U21(mark(z0), z1, z2)))
   A__U12(tt, U22(z0, z1, z2), tt) -> c2(A__PLUS(tt, a__U22(mark(z0), z1, z2)))
   A__U12(tt, x(z0, z1), tt) -> c2(A__PLUS(tt, a__x(mark(z0), mark(z1))))
   A__U12(tt, tt, tt) -> c2(A__PLUS(tt, tt))
   A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0))

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

(202)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3)))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3)))
   A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U12(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(U22(x1, x2, x3)))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), 0), MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c2(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(U22(x1, z1, z2)))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c2(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(U22(tt, x2, x3)))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c2(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(U22(s(z0), x2, x3)))
   A__U12(tt, tt, U22(x1, x2, x3)) -> c2(MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(0, x2, x3)) -> c2(A__PLUS(a__U22(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U12(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U12(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U12(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U12(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U12(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U12(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U12(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U12(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U12(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2))))
   A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2))))
   A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U12(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U12(tt, x0, s(U22(z0, z1, z2))) -> c2(A__PLUS(s(a__U22(mark(z0), z1, z2)), mark(x0)), MARK(s(U22(z0, z1, z2))))
   A__U12(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, tt, tt) -> c2(A__PLUS(tt, tt))
   A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
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   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
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   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
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   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
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   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
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   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
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   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
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   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
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   A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U12(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(U22(x1, x2, x3)))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), 0), MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c2(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(U22(x1, z1, z2)))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c2(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(U22(tt, x2, x3)))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c2(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(U22(s(z0), x2, x3)))
   A__U12(tt, tt, U22(x1, x2, x3)) -> c2(MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(0, x2, x3)) -> c2(A__PLUS(a__U22(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U12(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U12(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U12(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U12(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U12(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U12(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U12(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U12(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U12(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2))))
   A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2))))
   A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U12(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U12(tt, x0, s(U22(z0, z1, z2))) -> c2(A__PLUS(s(a__U22(mark(z0), z1, z2)), mark(x0)), MARK(s(U22(z0, z1, z2))))
   A__U12(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, tt, tt) -> c2(A__PLUS(tt, tt))
   A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(203) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   A__U12(tt, tt, tt) -> c2(A__PLUS(tt, tt))

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

(204)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
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   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U12(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(U22(x1, x2, x3)))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), 0), MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c2(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(U22(x1, z1, z2)))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c2(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(U22(tt, x2, x3)))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c2(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(U22(s(z0), x2, x3)))
   A__U12(tt, tt, U22(x1, x2, x3)) -> c2(MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(0, x2, x3)) -> c2(A__PLUS(a__U22(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U12(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U12(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U12(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U12(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U12(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U12(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U12(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U12(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U12(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2))))
   A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2))))
   A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U12(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U12(tt, x0, s(U22(z0, z1, z2))) -> c2(A__PLUS(s(a__U22(mark(z0), z1, z2)), mark(x0)), MARK(s(U22(z0, z1, z2))))
   A__U12(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0)))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
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   A__U12(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U12(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U12(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U12(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U12(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U12(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U12(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U12(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U12(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2))))
   A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2))))
   A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U12(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U12(tt, x0, s(U22(z0, z1, z2))) -> c2(A__PLUS(s(a__U22(mark(z0), z1, z2)), mark(x0)), MARK(s(U22(z0, z1, z2))))
   A__U12(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(205) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, x0, 0) -> c2(A__PLUS(0, mark(x0))) by 
   A__U12(tt, U11(z0, z1, z2), 0) -> c2(A__PLUS(0, a__U11(mark(z0), z1, z2)))
   A__U12(tt, U12(z0, z1, z2), 0) -> c2(A__PLUS(0, a__U12(mark(z0), z1, z2)))
   A__U12(tt, plus(z0, z1), 0) -> c2(A__PLUS(0, a__plus(mark(z0), mark(z1))))
   A__U12(tt, U21(z0, z1, z2), 0) -> c2(A__PLUS(0, a__U21(mark(z0), z1, z2)))
   A__U12(tt, U22(z0, z1, z2), 0) -> c2(A__PLUS(0, a__U22(mark(z0), z1, z2)))
   A__U12(tt, x(z0, z1), 0) -> c2(A__PLUS(0, a__x(mark(z0), mark(z1))))
   A__U12(tt, tt, 0) -> c2(A__PLUS(0, tt))
   A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0))

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

(206)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
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   A__U12(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U12(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U12(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U12(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U12(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U12(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2))))
   A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2))))
   A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U12(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U12(tt, x0, s(U22(z0, z1, z2))) -> c2(A__PLUS(s(a__U22(mark(z0), z1, z2)), mark(x0)), MARK(s(U22(z0, z1, z2))))
   A__U12(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0))
   A__U12(tt, tt, 0) -> c2(A__PLUS(0, tt))
   A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
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   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U11(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U11(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c2(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(U11(tt, x2, x3)))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3)))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2)))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3)))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3)))
   A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U12(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(U22(x1, x2, x3)))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), 0), MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c2(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(U22(x1, z1, z2)))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c2(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(U22(tt, x2, x3)))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c2(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(U22(s(z0), x2, x3)))
   A__U12(tt, tt, U22(x1, x2, x3)) -> c2(MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(0, x2, x3)) -> c2(A__PLUS(a__U22(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U12(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U12(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U12(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U12(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U12(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U12(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U12(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U12(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U12(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2))))
   A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2))))
   A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U12(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U12(tt, x0, s(U22(z0, z1, z2))) -> c2(A__PLUS(s(a__U22(mark(z0), z1, z2)), mark(x0)), MARK(s(U22(z0, z1, z2))))
   A__U12(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0))
   A__U12(tt, tt, 0) -> c2(A__PLUS(0, tt))
   A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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(207) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   A__U12(tt, tt, 0) -> c2(A__PLUS(0, tt))

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

(208)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
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   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c2(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(U11(s(z0), x2, x3)))
   A__U12(tt, tt, U11(x1, x2, x3)) -> c2(MARK(U11(x1, x2, x3)))
   A__U12(tt, x0, U11(0, x2, x3)) -> c2(A__PLUS(a__U11(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(U12(x1, x2, x3)))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c2(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c2(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(U12(x1, z1, z2)))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U12(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3)))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3)))
   A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U12(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(U22(x1, x2, x3)))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), 0), MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c2(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(U22(x1, z1, z2)))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c2(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(U22(tt, x2, x3)))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c2(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(U22(s(z0), x2, x3)))
   A__U12(tt, tt, U22(x1, x2, x3)) -> c2(MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(0, x2, x3)) -> c2(A__PLUS(a__U22(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U12(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U12(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U12(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U12(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U12(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U12(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U12(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U12(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U12(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2))))
   A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2))))
   A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U12(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U12(tt, x0, s(U22(z0, z1, z2))) -> c2(A__PLUS(s(a__U22(mark(z0), z1, z2)), mark(x0)), MARK(s(U22(z0, z1, z2))))
   A__U12(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0))
   A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
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   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U12(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(U22(x1, x2, x3)))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), 0), MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c2(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(U22(x1, z1, z2)))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c2(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(U22(tt, x2, x3)))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c2(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(U22(s(z0), x2, x3)))
   A__U12(tt, tt, U22(x1, x2, x3)) -> c2(MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(0, x2, x3)) -> c2(A__PLUS(a__U22(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U12(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U12(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U12(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U12(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U12(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U12(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U12(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U12(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U12(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2))))
   A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2))))
   A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U12(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U12(tt, x0, s(U22(z0, z1, z2))) -> c2(A__PLUS(s(a__U22(mark(z0), z1, z2)), mark(x0)), MARK(s(U22(z0, z1, z2))))
   A__U12(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0))
   A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(209) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, U11(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2))) by 
   A__U12(tt, U11(x0, z1, z2), x3) -> c3(A__PLUS(mark(x3), U11(mark(x0), z1, z2)), MARK(U11(x0, z1, z2)))
   A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2)))
   A__U12(tt, U11(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U11(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U11(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U11(x(z0, z1), x1, x2)))
   A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2)))
   A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2)))
   A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(U11(0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))

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

(210)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
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   A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U12(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(U22(x1, x2, x3)))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), 0), MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c2(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(U22(x1, z1, z2)))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c2(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(U22(tt, x2, x3)))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c2(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(U22(s(z0), x2, x3)))
   A__U12(tt, tt, U22(x1, x2, x3)) -> c2(MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(0, x2, x3)) -> c2(A__PLUS(a__U22(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U12(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U12(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U12(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U12(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U12(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U12(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U12(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U12(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U12(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2))))
   A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2))))
   A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U12(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U12(tt, x0, s(U22(z0, z1, z2))) -> c2(A__PLUS(s(a__U22(mark(z0), z1, z2)), mark(x0)), MARK(s(U22(z0, z1, z2))))
   A__U12(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0))
   A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0))
   A__U12(tt, U11(x0, z1, z2), x3) -> c3(A__PLUS(mark(x3), U11(mark(x0), z1, z2)), MARK(U11(x0, z1, z2)))
   A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2)))
   A__U12(tt, U11(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U11(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U11(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U11(x(z0, z1), x1, x2)))
   A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2)))
   A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2)))
   A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(U11(0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
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   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
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   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
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   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
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   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
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   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
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   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
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   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
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   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
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   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
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   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
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   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U12(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(U22(x1, x2, x3)))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), 0), MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c2(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(U22(x1, z1, z2)))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c2(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(U22(tt, x2, x3)))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c2(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(U22(s(z0), x2, x3)))
   A__U12(tt, tt, U22(x1, x2, x3)) -> c2(MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(0, x2, x3)) -> c2(A__PLUS(a__U22(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U12(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U12(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U12(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U12(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U12(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U12(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U12(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U12(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U12(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2))))
   A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2))))
   A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U12(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U12(tt, x0, s(U22(z0, z1, z2))) -> c2(A__PLUS(s(a__U22(mark(z0), z1, z2)), mark(x0)), MARK(s(U22(z0, z1, z2))))
   A__U12(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0))
   A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0))
   A__U12(tt, U11(x0, z1, z2), x3) -> c3(A__PLUS(mark(x3), U11(mark(x0), z1, z2)), MARK(U11(x0, z1, z2)))
   A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2)))
   A__U12(tt, U11(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U11(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U11(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U11(x(z0, z1), x1, x2)))
   A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2)))
   A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2)))
   A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2)), MARK(U11(0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

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

(212)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
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   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U12(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c2(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(U12(tt, x2, x3)))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c2(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(U12(s(z0), x2, x3)))
   A__U12(tt, tt, U12(x1, x2, x3)) -> c2(MARK(U12(x1, x2, x3)))
   A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U12(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(U22(x1, x2, x3)))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), 0), MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c2(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(U22(x1, z1, z2)))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c2(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(U22(tt, x2, x3)))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c2(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(U22(s(z0), x2, x3)))
   A__U12(tt, tt, U22(x1, x2, x3)) -> c2(MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(0, x2, x3)) -> c2(A__PLUS(a__U22(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U12(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U12(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U12(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U12(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U12(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U12(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U12(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U12(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U12(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2))))
   A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2))))
   A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U12(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U12(tt, x0, s(U22(z0, z1, z2))) -> c2(A__PLUS(s(a__U22(mark(z0), z1, z2)), mark(x0)), MARK(s(U22(z0, z1, z2))))
   A__U12(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0))
   A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0))
   A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2)))
   A__U12(tt, U11(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U11(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U11(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U11(x(z0, z1), x1, x2)))
   A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2)))
   A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2)))
   A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
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   MARK(s(z0)) -> c26(MARK(z0))
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   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
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   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
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   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
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   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
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   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
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   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
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   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
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   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
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   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
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   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
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   A__U12(tt, x0, U12(0, x2, x3)) -> c2(A__PLUS(a__U12(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U12(tt, 0, plus(x1, x2)) -> c2(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, x2)) -> c2(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c2(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, x(z0, z1))))
   A__U12(tt, x0, plus(x1, tt)) -> c2(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U12(tt, x0, plus(x1, s(z0))) -> c2(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U12(tt, x0, plus(x1, 0)) -> c2(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c2(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(x(z0, z1), x2)))
   A__U12(tt, x0, plus(tt, x2)) -> c2(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U12(tt, x0, plus(s(z0), x2)) -> c2(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U12(tt, x0, plus(0, x2)) -> c2(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U12(tt, tt, plus(x1, x2)) -> c2(MARK(plus(x1, x2)))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(U21(x1, x2, x3)))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c2(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c2(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(U21(x1, z1, z2)))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U21(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U12(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(U22(x1, x2, x3)))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), 0), MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c2(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(U22(x1, z1, z2)))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c2(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(U22(tt, x2, x3)))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c2(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(U22(s(z0), x2, x3)))
   A__U12(tt, tt, U22(x1, x2, x3)) -> c2(MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(0, x2, x3)) -> c2(A__PLUS(a__U22(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U12(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U12(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U12(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U12(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U12(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U12(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U12(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U12(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U12(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2))))
   A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2))))
   A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U12(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U12(tt, x0, s(U22(z0, z1, z2))) -> c2(A__PLUS(s(a__U22(mark(z0), z1, z2)), mark(x0)), MARK(s(U22(z0, z1, z2))))
   A__U12(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0))
   A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0))
   A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2)))
   A__U12(tt, U11(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U11(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U11(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U11(x(z0, z1), x1, x2)))
   A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2)))
   A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2)))
   A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(213) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, U12(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2))) by 
   A__U12(tt, U12(x0, z1, z2), x3) -> c3(A__PLUS(mark(x3), U12(mark(x0), z1, z2)), MARK(U12(x0, z1, z2)))
   A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2)))
   A__U12(tt, U12(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U12(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U12(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U12(x(z0, z1), x1, x2)))
   A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2)))
   A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2)))
   A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(U12(0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))

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

(214)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
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   A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0))
   A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0))
   A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2)))
   A__U12(tt, U11(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U11(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U11(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U11(x(z0, z1), x1, x2)))
   A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2)))
   A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2)))
   A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2)))
   A__U12(tt, U12(x0, z1, z2), x3) -> c3(A__PLUS(mark(x3), U12(mark(x0), z1, z2)), MARK(U12(x0, z1, z2)))
   A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2)))
   A__U12(tt, U12(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U12(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U12(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U12(x(z0, z1), x1, x2)))
   A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2)))
   A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2)))
   A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(U12(0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
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   A__U12(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U12(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U12(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U12(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U12(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U12(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2))))
   A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2))))
   A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U12(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U12(tt, x0, s(U22(z0, z1, z2))) -> c2(A__PLUS(s(a__U22(mark(z0), z1, z2)), mark(x0)), MARK(s(U22(z0, z1, z2))))
   A__U12(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0))
   A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0))
   A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2)))
   A__U12(tt, U11(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U11(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U11(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U11(x(z0, z1), x1, x2)))
   A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2)))
   A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2)))
   A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2)))
   A__U12(tt, U12(x0, z1, z2), x3) -> c3(A__PLUS(mark(x3), U12(mark(x0), z1, z2)), MARK(U12(x0, z1, z2)))
   A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2)))
   A__U12(tt, U12(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U12(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U12(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U12(x(z0, z1), x1, x2)))
   A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2)))
   A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2)))
   A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2)), MARK(U12(0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

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

(216)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
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   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U21(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c2(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(U21(tt, x2, x3)))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c2(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(U21(s(z0), x2, x3)))
   A__U12(tt, tt, U21(x1, x2, x3)) -> c2(MARK(U21(x1, x2, x3)))
   A__U12(tt, x0, U21(0, x2, x3)) -> c2(A__PLUS(a__U21(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(U22(x1, x2, x3)))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c2(A__PLUS(a__U22(mark(x1), x2, x3), 0), MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c2(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(U22(x1, z1, z2)))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U11(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U12(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(plus(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U21(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c2(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U22(U22(z0, z1, z2), x2, x3)))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c2(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U22(x(z0, z1), x2, x3)))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c2(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(U22(tt, x2, x3)))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c2(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(U22(s(z0), x2, x3)))
   A__U12(tt, tt, U22(x1, x2, x3)) -> c2(MARK(U22(x1, x2, x3)))
   A__U12(tt, x0, U22(0, x2, x3)) -> c2(A__PLUS(a__U22(0, x2, x3), mark(x0)))
   A__U12(tt, s(z0), x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(x(x1, x2)))
   A__U12(tt, 0, x(x1, x2)) -> c2(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, x2)) -> c2(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x(x1, x2)))
   A__U12(tt, x0, x(x1, U11(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U11(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U12(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U12(z0, z1, z2))))
   A__U12(tt, x0, x(x1, plus(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, plus(z0, z1))))
   A__U12(tt, x0, x(x1, U21(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U21(z0, z1, z2))))
   A__U12(tt, x0, x(x1, U22(z0, z1, z2))) -> c2(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x(x1, U22(z0, z1, z2))))
   A__U12(tt, x0, x(x1, x(z0, z1))) -> c2(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x(x1, x(z0, z1))))
   A__U12(tt, x0, x(x1, tt)) -> c2(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x(x1, tt)))
   A__U12(tt, x0, x(x1, s(z0))) -> c2(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x(x1, s(z0))))
   A__U12(tt, x0, x(x1, 0)) -> c2(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x(x1, 0)))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U11(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U12(z0, z1, z2), x2)))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c2(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(plus(z0, z1), x2)))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U21(z0, z1, z2), x2)))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U12(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U12(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U12(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U12(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2))))
   A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2))))
   A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U12(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U12(tt, x0, s(U22(z0, z1, z2))) -> c2(A__PLUS(s(a__U22(mark(z0), z1, z2)), mark(x0)), MARK(s(U22(z0, z1, z2))))
   A__U12(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0))
   A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0))
   A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2)))
   A__U12(tt, U11(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U11(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U11(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U11(x(z0, z1), x1, x2)))
   A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2)))
   A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2)))
   A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2)))
   A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2)))
   A__U12(tt, U12(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U12(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U12(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U12(x(z0, z1), x1, x2)))
   A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2)))
   A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2)))
   A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c19(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1, z2), x1)) -> c19(A__PLUS(a__U11(mark(z0), z1, z2), mark(x1)), MARK(U11(z0, z1, z2)))
   MARK(plus(U12(z0, z1, z2), x1)) -> c19(A__PLUS(a__U12(mark(z0), z1, z2), mark(x1)), MARK(U12(z0, z1, z2)))
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   A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2)))
   A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(217) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, plus(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) by 
   A__U12(tt, plus(x0, x1), x2) -> c3(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2))))
   A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2))))
   A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1))))
   A__U12(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2))))
   A__U12(tt, plus(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0), z1, z2))), MARK(plus(x0, U22(z0, z1, z2))))
   A__U12(tt, plus(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(plus(x0, x(z0, z1))))
   A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt)))
   A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0))))
   A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0)))
   A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1)))
   A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1)))
   A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U12(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1)))
   A__U12(tt, plus(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U22(mark(z0), z1, z2), mark(x1))), MARK(plus(U22(z0, z1, z2), x1)))
   A__U12(tt, plus(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(plus(x(z0, z1), x1)))
   A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))

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

(218)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
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   A__U12(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U12(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U12(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U12(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U12(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2))))
   A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2))))
   A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U12(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U12(tt, x0, s(U22(z0, z1, z2))) -> c2(A__PLUS(s(a__U22(mark(z0), z1, z2)), mark(x0)), MARK(s(U22(z0, z1, z2))))
   A__U12(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0))
   A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0))
   A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2)))
   A__U12(tt, U11(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U11(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U11(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U11(x(z0, z1), x1, x2)))
   A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2)))
   A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2)))
   A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2)))
   A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2)))
   A__U12(tt, U12(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U12(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U12(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U12(x(z0, z1), x1, x2)))
   A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2)))
   A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2)))
   A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2)))
   A__U12(tt, plus(x0, x1), x2) -> c3(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2))))
   A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2))))
   A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1))))
   A__U12(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2))))
   A__U12(tt, plus(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0), z1, z2))), MARK(plus(x0, U22(z0, z1, z2))))
   A__U12(tt, plus(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(plus(x0, x(z0, z1))))
   A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt)))
   A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0))))
   A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0)))
   A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1)))
   A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1)))
   A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U12(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1)))
   A__U12(tt, plus(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U22(mark(z0), z1, z2), mark(x1))), MARK(plus(U22(z0, z1, z2), x1)))
   A__U12(tt, plus(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(plus(x(z0, z1), x1)))
   A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
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   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
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   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   A__U12(tt, plus(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(plus(x0, x(z0, z1))))
   A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt)))
   A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0))))
   A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0)))
   A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1)))
   A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1)))
   A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U12(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1)))
   A__U12(tt, plus(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U22(mark(z0), z1, z2), mark(x1))), MARK(plus(U22(z0, z1, z2), x1)))
   A__U12(tt, plus(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(plus(x(z0, z1), x1)))
   A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

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

(220)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
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   A__U12(tt, x0, s(U22(z0, z1, z2))) -> c2(A__PLUS(s(a__U22(mark(z0), z1, z2)), mark(x0)), MARK(s(U22(z0, z1, z2))))
   A__U12(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0))
   A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0))
   A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2)))
   A__U12(tt, U11(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U11(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U11(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U11(x(z0, z1), x1, x2)))
   A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2)))
   A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2)))
   A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2)))
   A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2)))
   A__U12(tt, U12(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U12(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U12(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U12(x(z0, z1), x1, x2)))
   A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2)))
   A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2)))
   A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2)))
   A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2))))
   A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2))))
   A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1))))
   A__U12(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2))))
   A__U12(tt, plus(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0), z1, z2))), MARK(plus(x0, U22(z0, z1, z2))))
   A__U12(tt, plus(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(plus(x0, x(z0, z1))))
   A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt)))
   A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0))))
   A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0)))
   A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1)))
   A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1)))
   A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U12(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1)))
   A__U12(tt, plus(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U22(mark(z0), z1, z2), mark(x1))), MARK(plus(U22(z0, z1, z2), x1)))
   A__U12(tt, plus(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(plus(x(z0, z1), x1)))
   A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
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   A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(221) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, U21(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2))) by 
   A__U12(tt, U21(x0, z1, z2), x3) -> c3(A__PLUS(mark(x3), U21(mark(x0), z1, z2)), MARK(U21(x0, z1, z2)))
   A__U12(tt, U21(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U21(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U21(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2)))
   A__U12(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U21(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U21(x(z0, z1), x1, x2)))
   A__U12(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2)))
   A__U12(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2)))
   A__U12(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(U21(0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))

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

(222)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
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   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c2(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x(U22(z0, z1, z2), x2)))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c2(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x(x(z0, z1), x2)))
   A__U12(tt, x0, x(tt, x2)) -> c2(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x(tt, x2)))
   A__U12(tt, x0, x(s(z0), x2)) -> c2(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x(s(z0), x2)))
   A__U12(tt, x0, x(0, x2)) -> c2(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x(0, x2)))
   A__U12(tt, tt, x(x1, x2)) -> c2(MARK(x(x1, x2)))
   A__U12(tt, s(z0), s(x1)) -> c2(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U12(tt, 0, s(x1)) -> c2(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U12(tt, x0, s(U11(z0, z1, z2))) -> c2(A__PLUS(s(a__U11(mark(z0), z1, z2)), mark(x0)), MARK(s(U11(z0, z1, z2))))
   A__U12(tt, x0, s(U12(z0, z1, z2))) -> c2(A__PLUS(s(a__U12(mark(z0), z1, z2)), mark(x0)), MARK(s(U12(z0, z1, z2))))
   A__U12(tt, x0, s(plus(z0, z1))) -> c2(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U12(tt, x0, s(U21(z0, z1, z2))) -> c2(A__PLUS(s(a__U21(mark(z0), z1, z2)), mark(x0)), MARK(s(U21(z0, z1, z2))))
   A__U12(tt, x0, s(U22(z0, z1, z2))) -> c2(A__PLUS(s(a__U22(mark(z0), z1, z2)), mark(x0)), MARK(s(U22(z0, z1, z2))))
   A__U12(tt, x0, s(x(z0, z1))) -> c2(A__PLUS(s(a__x(mark(z0), mark(z1))), mark(x0)), MARK(s(x(z0, z1))))
   A__U12(tt, x0, s(tt)) -> c2(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0))
   A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0))
   A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2)))
   A__U12(tt, U11(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U11(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U11(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U11(x(z0, z1), x1, x2)))
   A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2)))
   A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2)))
   A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2)))
   A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2)))
   A__U12(tt, U12(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U12(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U12(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U12(x(z0, z1), x1, x2)))
   A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2)))
   A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2)))
   A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2)))
   A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2))))
   A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2))))
   A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1))))
   A__U12(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2))))
   A__U12(tt, plus(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0), z1, z2))), MARK(plus(x0, U22(z0, z1, z2))))
   A__U12(tt, plus(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(plus(x0, x(z0, z1))))
   A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt)))
   A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0))))
   A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0)))
   A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1)))
   A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1)))
   A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U12(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1)))
   A__U12(tt, plus(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U22(mark(z0), z1, z2), mark(x1))), MARK(plus(U22(z0, z1, z2), x1)))
   A__U12(tt, plus(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(plus(x(z0, z1), x1)))
   A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1)))
   A__U12(tt, U21(x0, z1, z2), x3) -> c3(A__PLUS(mark(x3), U21(mark(x0), z1, z2)), MARK(U21(x0, z1, z2)))
   A__U12(tt, U21(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U21(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U21(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2)))
   A__U12(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U21(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U21(x(z0, z1), x1, x2)))
   A__U12(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2)))
   A__U12(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2)))
   A__U12(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(U21(0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
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   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
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   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
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   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
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   A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2)))
   A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2)))
   A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2)))
   A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2))))
   A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2))))
   A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1))))
   A__U12(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2))))
   A__U12(tt, plus(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0), z1, z2))), MARK(plus(x0, U22(z0, z1, z2))))
   A__U12(tt, plus(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(plus(x0, x(z0, z1))))
   A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt)))
   A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0))))
   A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0)))
   A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1)))
   A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1)))
   A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U12(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1)))
   A__U12(tt, plus(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U22(mark(z0), z1, z2), mark(x1))), MARK(plus(U22(z0, z1, z2), x1)))
   A__U12(tt, plus(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(plus(x(z0, z1), x1)))
   A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1)))
   A__U12(tt, U21(x0, z1, z2), x3) -> c3(A__PLUS(mark(x3), U21(mark(x0), z1, z2)), MARK(U21(x0, z1, z2)))
   A__U12(tt, U21(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U21(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U21(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2)))
   A__U12(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U21(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U21(x(z0, z1), x1, x2)))
   A__U12(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2)))
   A__U12(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2)))
   A__U12(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)), MARK(U21(0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

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

(224)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
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   A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1)))
   A__U12(tt, U21(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U21(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U21(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2)))
   A__U12(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U21(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U21(x(z0, z1), x1, x2)))
   A__U12(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2)))
   A__U12(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2)))
   A__U12(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
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   A__U12(tt, x0, s(s(z0))) -> c2(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U12(tt, x0, s(0)) -> c2(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U12(tt, x0, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, tt, s(x1)) -> c2(MARK(s(x1)))
   A__U12(tt, s(z0), tt) -> c2(A__PLUS(tt, s(mark(z0))))
   A__U12(tt, 0, tt) -> c2(A__PLUS(tt, 0))
   A__U12(tt, s(z0), 0) -> c2(A__PLUS(0, s(mark(z0))))
   A__U12(tt, 0, 0) -> c2(A__PLUS(0, 0))
   A__U12(tt, U11(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U11(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U11(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U11(plus(z0, z1), x1, x2)))
   A__U12(tt, U11(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U11(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U11(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U11(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U11(x(z0, z1), x1, x2)))
   A__U12(tt, U11(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(tt, x1, x2)), MARK(U11(tt, x1, x2)))
   A__U12(tt, U11(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(s(mark(z0)), x1, x2)), MARK(U11(s(z0), x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2)))
   A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2)))
   A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2)))
   A__U12(tt, U12(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U12(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U12(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U12(x(z0, z1), x1, x2)))
   A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2)))
   A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2)))
   A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2)))
   A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2))))
   A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2))))
   A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1))))
   A__U12(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2))))
   A__U12(tt, plus(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0), z1, z2))), MARK(plus(x0, U22(z0, z1, z2))))
   A__U12(tt, plus(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(plus(x0, x(z0, z1))))
   A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt)))
   A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0))))
   A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0)))
   A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1)))
   A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1)))
   A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U12(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1)))
   A__U12(tt, plus(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U22(mark(z0), z1, z2), mark(x1))), MARK(plus(U22(z0, z1, z2), x1)))
   A__U12(tt, plus(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(plus(x(z0, z1), x1)))
   A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1)))
   A__U12(tt, U21(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U21(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U21(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2)))
   A__U12(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U21(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U21(x(z0, z1), x1, x2)))
   A__U12(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2)))
   A__U12(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2)))
   A__U12(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(225) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, U22(z0, z1, z2), x1) -> c3(A__PLUS(mark(x1), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2))) by 
   A__U12(tt, U22(x0, z1, z2), x3) -> c3(A__PLUS(mark(x3), U22(mark(x0), z1, z2)), MARK(U22(x0, z1, z2)))
   A__U12(tt, U22(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U22(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U22(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U22(plus(z0, z1), x1, x2)))
   A__U12(tt, U22(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U22(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U22(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U22(x(z0, z1), x1, x2)))
   A__U12(tt, U22(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(U22(tt, x1, x2)))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(U22(s(z0), x1, x2)))
   A__U12(tt, U22(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(0, x1, x2)), MARK(U22(0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))

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

(226)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
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   A__U12(tt, U11(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U11(mark(x0), x1, x2)), MARK(U11(x0, x1, x2)))
   A__U12(tt, U11(x0, z1, z2), x3) -> c3(MARK(U11(x0, z1, z2)))
   A__U12(tt, U11(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U11(0, x1, x2)))
   A__U12(tt, U12(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U12(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U12(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U12(plus(z0, z1), x1, x2)))
   A__U12(tt, U12(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U12(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U12(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U12(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U12(x(z0, z1), x1, x2)))
   A__U12(tt, U12(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(tt, x1, x2)), MARK(U12(tt, x1, x2)))
   A__U12(tt, U12(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(s(mark(z0)), x1, x2)), MARK(U12(s(z0), x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2)))
   A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2)))
   A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2))))
   A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2))))
   A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1))))
   A__U12(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2))))
   A__U12(tt, plus(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0), z1, z2))), MARK(plus(x0, U22(z0, z1, z2))))
   A__U12(tt, plus(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(plus(x0, x(z0, z1))))
   A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt)))
   A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0))))
   A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0)))
   A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1)))
   A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1)))
   A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U12(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1)))
   A__U12(tt, plus(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U22(mark(z0), z1, z2), mark(x1))), MARK(plus(U22(z0, z1, z2), x1)))
   A__U12(tt, plus(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(plus(x(z0, z1), x1)))
   A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1)))
   A__U12(tt, U21(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U21(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U21(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2)))
   A__U12(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U21(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U21(x(z0, z1), x1, x2)))
   A__U12(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2)))
   A__U12(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2)))
   A__U12(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c3(A__PLUS(mark(x3), U22(mark(x0), z1, z2)), MARK(U22(x0, z1, z2)))
   A__U12(tt, U22(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U22(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U22(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U22(plus(z0, z1), x1, x2)))
   A__U12(tt, U22(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U22(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U22(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U22(x(z0, z1), x1, x2)))
   A__U12(tt, U22(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(U22(tt, x1, x2)))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(U22(s(z0), x1, x2)))
   A__U12(tt, U22(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(0, x1, x2)), MARK(U22(0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
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   A__U12(tt, U12(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2)))
   A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2)))
   A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2))))
   A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2))))
   A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1))))
   A__U12(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2))))
   A__U12(tt, plus(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0), z1, z2))), MARK(plus(x0, U22(z0, z1, z2))))
   A__U12(tt, plus(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(plus(x0, x(z0, z1))))
   A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt)))
   A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0))))
   A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0)))
   A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1)))
   A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1)))
   A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U12(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1)))
   A__U12(tt, plus(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U22(mark(z0), z1, z2), mark(x1))), MARK(plus(U22(z0, z1, z2), x1)))
   A__U12(tt, plus(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(plus(x(z0, z1), x1)))
   A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1)))
   A__U12(tt, U21(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U21(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U21(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2)))
   A__U12(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U21(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U21(x(z0, z1), x1, x2)))
   A__U12(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2)))
   A__U12(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2)))
   A__U12(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c3(A__PLUS(mark(x3), U22(mark(x0), z1, z2)), MARK(U22(x0, z1, z2)))
   A__U12(tt, U22(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U22(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U22(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U22(plus(z0, z1), x1, x2)))
   A__U12(tt, U22(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U22(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U22(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U22(x(z0, z1), x1, x2)))
   A__U12(tt, U22(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(U22(tt, x1, x2)))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(U22(s(z0), x1, x2)))
   A__U12(tt, U22(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(0, x1, x2)), MARK(U22(0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

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

(228)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
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   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
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   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
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   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
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   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
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   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
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   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
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   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
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   MARK(plus(s(z0), x1)) -> c19(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
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   MARK(plus(tt, x1)) -> c19(A__PLUS(tt, mark(x1)))
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   A__U12(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2))))
   A__U12(tt, plus(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0), z1, z2))), MARK(plus(x0, U22(z0, z1, z2))))
   A__U12(tt, plus(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(plus(x0, x(z0, z1))))
   A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt)))
   A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0))))
   A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0)))
   A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1)))
   A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1)))
   A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U12(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1)))
   A__U12(tt, plus(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U22(mark(z0), z1, z2), mark(x1))), MARK(plus(U22(z0, z1, z2), x1)))
   A__U12(tt, plus(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(plus(x(z0, z1), x1)))
   A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1)))
   A__U12(tt, U21(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U21(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U21(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2)))
   A__U12(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U21(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U21(x(z0, z1), x1, x2)))
   A__U12(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2)))
   A__U12(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2)))
   A__U12(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)))
   A__U12(tt, U22(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U22(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U22(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U22(plus(z0, z1), x1, x2)))
   A__U12(tt, U22(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U22(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U22(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U22(x(z0, z1), x1, x2)))
   A__U12(tt, U22(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(U22(tt, x1, x2)))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(U22(s(z0), x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c3(MARK(U22(x0, z1, z2)))
   A__U12(tt, U22(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(0, x1, x2)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
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   A__U12(tt, U21(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U21(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2)))
   A__U12(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U21(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U21(x(z0, z1), x1, x2)))
   A__U12(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2)))
   A__U12(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2)))
   A__U12(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)))
   A__U12(tt, U22(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U22(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U22(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U22(plus(z0, z1), x1, x2)))
   A__U12(tt, U22(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U22(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U22(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U22(x(z0, z1), x1, x2)))
   A__U12(tt, U22(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(U22(tt, x1, x2)))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(U22(s(z0), x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c3(MARK(U22(x0, z1, z2)))
   A__U12(tt, U22(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(0, x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(229) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, x(z0, z1), x1) -> c3(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) by 
   A__U12(tt, x(x0, x1), x2) -> c3(A__PLUS(mark(x2), x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x(x0, U11(z0, z1, z2))))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x(x0, U12(z0, z1, z2))))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x(x0, plus(z0, z1))))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x(x0, U21(z0, z1, z2))))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x(x0, U22(z0, z1, z2))))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x(x0, x(z0, z1))))
   A__U12(tt, x(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x(x0, tt)))
   A__U12(tt, x(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x(x0, s(z0))))
   A__U12(tt, x(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x(x0, 0)))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x(U11(z0, z1, z2), x1)))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x(U12(z0, z1, z2), x1)))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x(plus(z0, z1), x1)))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x(U21(z0, z1, z2), x1)))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x(U22(z0, z1, z2), x1)))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x(x(z0, z1), x1)))
   A__U12(tt, x(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x(tt, x1)))
   A__U12(tt, x(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x(s(z0), x1)))
   A__U12(tt, x(0, x1), x2) -> c3(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x(0, x1)))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), tt) -> c3(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))

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

(230)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
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   A__U12(tt, plus(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U22(mark(z0), z1, z2), mark(x1))), MARK(plus(U22(z0, z1, z2), x1)))
   A__U12(tt, plus(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(plus(x(z0, z1), x1)))
   A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1)))
   A__U12(tt, U21(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U21(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U21(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2)))
   A__U12(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U21(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U21(x(z0, z1), x1, x2)))
   A__U12(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2)))
   A__U12(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2)))
   A__U12(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)))
   A__U12(tt, U22(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U22(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U22(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U22(plus(z0, z1), x1, x2)))
   A__U12(tt, U22(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U22(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U22(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U22(x(z0, z1), x1, x2)))
   A__U12(tt, U22(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(U22(tt, x1, x2)))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(U22(s(z0), x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c3(MARK(U22(x0, z1, z2)))
   A__U12(tt, U22(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(0, x1, x2)))
   A__U12(tt, x(x0, x1), x2) -> c3(A__PLUS(mark(x2), x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x(x0, U11(z0, z1, z2))))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x(x0, U12(z0, z1, z2))))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x(x0, plus(z0, z1))))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x(x0, U21(z0, z1, z2))))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x(x0, U22(z0, z1, z2))))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x(x0, x(z0, z1))))
   A__U12(tt, x(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x(x0, tt)))
   A__U12(tt, x(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x(x0, s(z0))))
   A__U12(tt, x(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x(x0, 0)))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x(U11(z0, z1, z2), x1)))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x(U12(z0, z1, z2), x1)))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x(plus(z0, z1), x1)))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x(U21(z0, z1, z2), x1)))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x(U22(z0, z1, z2), x1)))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x(x(z0, z1), x1)))
   A__U12(tt, x(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x(tt, x1)))
   A__U12(tt, x(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x(s(z0), x1)))
   A__U12(tt, x(0, x1), x2) -> c3(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x(0, x1)))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), tt) -> c3(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
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   A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1)))
   A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U12(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1)))
   A__U12(tt, plus(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U22(mark(z0), z1, z2), mark(x1))), MARK(plus(U22(z0, z1, z2), x1)))
   A__U12(tt, plus(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(plus(x(z0, z1), x1)))
   A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1)))
   A__U12(tt, U21(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U21(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U21(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2)))
   A__U12(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U21(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U21(x(z0, z1), x1, x2)))
   A__U12(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2)))
   A__U12(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2)))
   A__U12(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)))
   A__U12(tt, U22(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U22(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U22(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U22(plus(z0, z1), x1, x2)))
   A__U12(tt, U22(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U22(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U22(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U22(x(z0, z1), x1, x2)))
   A__U12(tt, U22(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(U22(tt, x1, x2)))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(U22(s(z0), x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c3(MARK(U22(x0, z1, z2)))
   A__U12(tt, U22(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(0, x1, x2)))
   A__U12(tt, x(x0, x1), x2) -> c3(A__PLUS(mark(x2), x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x(x0, U11(z0, z1, z2))))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x(x0, U12(z0, z1, z2))))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x(x0, plus(z0, z1))))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x(x0, U21(z0, z1, z2))))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x(x0, U22(z0, z1, z2))))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x(x0, x(z0, z1))))
   A__U12(tt, x(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x(x0, tt)))
   A__U12(tt, x(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x(x0, s(z0))))
   A__U12(tt, x(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x(x0, 0)))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x(U11(z0, z1, z2), x1)))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x(U12(z0, z1, z2), x1)))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x(plus(z0, z1), x1)))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x(U21(z0, z1, z2), x1)))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x(U22(z0, z1, z2), x1)))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x(x(z0, z1), x1)))
   A__U12(tt, x(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x(tt, x1)))
   A__U12(tt, x(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x(s(z0), x1)))
   A__U12(tt, x(0, x1), x2) -> c3(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x(0, x1)))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), tt) -> c3(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

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

(232)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
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   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
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   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
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   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
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   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
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   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
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   A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2)))
   A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2)))
   A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2))))
   A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2))))
   A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1))))
   A__U12(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2))))
   A__U12(tt, plus(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0), z1, z2))), MARK(plus(x0, U22(z0, z1, z2))))
   A__U12(tt, plus(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(plus(x0, x(z0, z1))))
   A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt)))
   A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0))))
   A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0)))
   A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1)))
   A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1)))
   A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U12(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1)))
   A__U12(tt, plus(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U22(mark(z0), z1, z2), mark(x1))), MARK(plus(U22(z0, z1, z2), x1)))
   A__U12(tt, plus(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(plus(x(z0, z1), x1)))
   A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1)))
   A__U12(tt, U21(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U21(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U21(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2)))
   A__U12(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U21(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U21(x(z0, z1), x1, x2)))
   A__U12(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2)))
   A__U12(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2)))
   A__U12(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)))
   A__U12(tt, U22(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U22(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U22(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U22(plus(z0, z1), x1, x2)))
   A__U12(tt, U22(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U22(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U22(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U22(x(z0, z1), x1, x2)))
   A__U12(tt, U22(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(U22(tt, x1, x2)))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(U22(s(z0), x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c3(MARK(U22(x0, z1, z2)))
   A__U12(tt, U22(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(0, x1, x2)))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x(x0, U11(z0, z1, z2))))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x(x0, U12(z0, z1, z2))))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x(x0, plus(z0, z1))))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x(x0, U21(z0, z1, z2))))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x(x0, U22(z0, z1, z2))))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x(x0, x(z0, z1))))
   A__U12(tt, x(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x(x0, tt)))
   A__U12(tt, x(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x(x0, s(z0))))
   A__U12(tt, x(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x(x0, 0)))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x(U11(z0, z1, z2), x1)))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x(U12(z0, z1, z2), x1)))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x(plus(z0, z1), x1)))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x(U21(z0, z1, z2), x1)))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x(U22(z0, z1, z2), x1)))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x(x(z0, z1), x1)))
   A__U12(tt, x(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x(tt, x1)))
   A__U12(tt, x(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x(s(z0), x1)))
   A__U12(tt, x(0, x1), x2) -> c3(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x(0, x1)))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), tt) -> c3(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x2) -> c3(MARK(x(x0, x1)))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
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   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
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   A__U12(tt, U12(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U12(mark(x0), x1, x2)), MARK(U12(x0, x1, x2)))
   A__U12(tt, U12(x0, z1, z2), x3) -> c3(MARK(U12(x0, z1, z2)))
   A__U12(tt, U12(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U12(0, x1, x2)))
   A__U12(tt, plus(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1, z2))), MARK(plus(x0, U11(z0, z1, z2))))
   A__U12(tt, plus(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0), z1, z2))), MARK(plus(x0, U12(z0, z1, z2))))
   A__U12(tt, plus(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1))))
   A__U12(tt, plus(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0), z1, z2))), MARK(plus(x0, U21(z0, z1, z2))))
   A__U12(tt, plus(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__U22(mark(z0), z1, z2))), MARK(plus(x0, U22(z0, z1, z2))))
   A__U12(tt, plus(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), a__x(mark(z0), mark(z1)))), MARK(plus(x0, x(z0, z1))))
   A__U12(tt, plus(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt)))
   A__U12(tt, plus(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0))))
   A__U12(tt, plus(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0)))
   A__U12(tt, plus(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1, z2), mark(x1))), MARK(plus(U11(z0, z1, z2), x1)))
   A__U12(tt, plus(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U12(mark(z0), z1, z2), mark(x1))), MARK(plus(U12(z0, z1, z2), x1)))
   A__U12(tt, plus(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U12(tt, plus(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U21(mark(z0), z1, z2), mark(x1))), MARK(plus(U21(z0, z1, z2), x1)))
   A__U12(tt, plus(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__U22(mark(z0), z1, z2), mark(x1))), MARK(plus(U22(z0, z1, z2), x1)))
   A__U12(tt, plus(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(a__x(mark(z0), mark(z1)), mark(x1))), MARK(plus(x(z0, z1), x1)))
   A__U12(tt, plus(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U12(tt, plus(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1)))
   A__U12(tt, U21(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U21(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U21(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2)))
   A__U12(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U21(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U21(x(z0, z1), x1, x2)))
   A__U12(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2)))
   A__U12(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2)))
   A__U12(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)))
   A__U12(tt, U22(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U22(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U22(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U22(plus(z0, z1), x1, x2)))
   A__U12(tt, U22(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U22(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U22(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U22(x(z0, z1), x1, x2)))
   A__U12(tt, U22(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(U22(tt, x1, x2)))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(U22(s(z0), x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c3(MARK(U22(x0, z1, z2)))
   A__U12(tt, U22(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(0, x1, x2)))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x(x0, U11(z0, z1, z2))))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x(x0, U12(z0, z1, z2))))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x(x0, plus(z0, z1))))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x(x0, U21(z0, z1, z2))))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x(x0, U22(z0, z1, z2))))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x(x0, x(z0, z1))))
   A__U12(tt, x(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x(x0, tt)))
   A__U12(tt, x(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x(x0, s(z0))))
   A__U12(tt, x(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x(x0, 0)))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x(U11(z0, z1, z2), x1)))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x(U12(z0, z1, z2), x1)))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x(plus(z0, z1), x1)))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x(U21(z0, z1, z2), x1)))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x(U22(z0, z1, z2), x1)))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x(x(z0, z1), x1)))
   A__U12(tt, x(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x(tt, x1)))
   A__U12(tt, x(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x(s(z0), x1)))
   A__U12(tt, x(0, x1), x2) -> c3(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x(0, x1)))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), tt) -> c3(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x2) -> c3(MARK(x(x0, x1)))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(233) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, x0, U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), mark(x0)), MARK(x0)) by 
   A__U12(tt, U11(z0, z1, z2), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, tt, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), tt), MARK(tt))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(0))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))

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

(234)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
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   A__U12(tt, U22(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(0, x1, x2)))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x(x0, U11(z0, z1, z2))))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x(x0, U12(z0, z1, z2))))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x(x0, plus(z0, z1))))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x(x0, U21(z0, z1, z2))))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x(x0, U22(z0, z1, z2))))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x(x0, x(z0, z1))))
   A__U12(tt, x(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x(x0, tt)))
   A__U12(tt, x(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x(x0, s(z0))))
   A__U12(tt, x(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x(x0, 0)))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x(U11(z0, z1, z2), x1)))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x(U12(z0, z1, z2), x1)))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x(plus(z0, z1), x1)))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x(U21(z0, z1, z2), x1)))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x(U22(z0, z1, z2), x1)))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x(x(z0, z1), x1)))
   A__U12(tt, x(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x(tt, x1)))
   A__U12(tt, x(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x(s(z0), x1)))
   A__U12(tt, x(0, x1), x2) -> c3(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x(0, x1)))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), tt) -> c3(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x2) -> c3(MARK(x(x0, x1)))
   A__U12(tt, tt, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), tt), MARK(tt))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(0))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
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   A__U12(tt, U22(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(U22(tt, x1, x2)))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(U22(s(z0), x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c3(MARK(U22(x0, z1, z2)))
   A__U12(tt, U22(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(0, x1, x2)))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x(x0, U11(z0, z1, z2))))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x(x0, U12(z0, z1, z2))))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x(x0, plus(z0, z1))))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x(x0, U21(z0, z1, z2))))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x(x0, U22(z0, z1, z2))))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x(x0, x(z0, z1))))
   A__U12(tt, x(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x(x0, tt)))
   A__U12(tt, x(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x(x0, s(z0))))
   A__U12(tt, x(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x(x0, 0)))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x(U11(z0, z1, z2), x1)))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x(U12(z0, z1, z2), x1)))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x(plus(z0, z1), x1)))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x(U21(z0, z1, z2), x1)))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x(U22(z0, z1, z2), x1)))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x(x(z0, z1), x1)))
   A__U12(tt, x(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x(tt, x1)))
   A__U12(tt, x(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x(s(z0), x1)))
   A__U12(tt, x(0, x1), x2) -> c3(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x(0, x1)))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), tt) -> c3(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x2) -> c3(MARK(x(x0, x1)))
   A__U12(tt, tt, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), tt), MARK(tt))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(0))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(235) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   A__U12(tt, tt, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), tt), MARK(tt))

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

(236)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
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   A__U12(tt, U21(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U21(U12(z0, z1, z2), x1, x2)))
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   A__U12(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U21(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U21(x(z0, z1), x1, x2)))
   A__U12(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2)))
   A__U12(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2)))
   A__U12(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)))
   A__U12(tt, U22(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U22(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U22(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U22(plus(z0, z1), x1, x2)))
   A__U12(tt, U22(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U22(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U22(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U22(x(z0, z1), x1, x2)))
   A__U12(tt, U22(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(U22(tt, x1, x2)))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(U22(s(z0), x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c3(MARK(U22(x0, z1, z2)))
   A__U12(tt, U22(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(0, x1, x2)))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x(x0, U11(z0, z1, z2))))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x(x0, U12(z0, z1, z2))))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x(x0, plus(z0, z1))))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x(x0, U21(z0, z1, z2))))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x(x0, U22(z0, z1, z2))))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x(x0, x(z0, z1))))
   A__U12(tt, x(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x(x0, tt)))
   A__U12(tt, x(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x(x0, s(z0))))
   A__U12(tt, x(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x(x0, 0)))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x(U11(z0, z1, z2), x1)))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x(U12(z0, z1, z2), x1)))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x(plus(z0, z1), x1)))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x(U21(z0, z1, z2), x1)))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x(U22(z0, z1, z2), x1)))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x(x(z0, z1), x1)))
   A__U12(tt, x(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x(tt, x1)))
   A__U12(tt, x(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x(s(z0), x1)))
   A__U12(tt, x(0, x1), x2) -> c3(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x(0, x1)))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), tt) -> c3(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x2) -> c3(MARK(x(x0, x1)))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(0))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
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   A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1)))
   A__U12(tt, U21(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U21(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U21(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2)))
   A__U12(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U21(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U21(x(z0, z1), x1, x2)))
   A__U12(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2)))
   A__U12(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2)))
   A__U12(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)))
   A__U12(tt, U22(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U22(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U22(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U22(plus(z0, z1), x1, x2)))
   A__U12(tt, U22(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U22(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U22(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U22(x(z0, z1), x1, x2)))
   A__U12(tt, U22(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(U22(tt, x1, x2)))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(U22(s(z0), x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c3(MARK(U22(x0, z1, z2)))
   A__U12(tt, U22(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(0, x1, x2)))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x(x0, U11(z0, z1, z2))))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x(x0, U12(z0, z1, z2))))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x(x0, plus(z0, z1))))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x(x0, U21(z0, z1, z2))))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x(x0, U22(z0, z1, z2))))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x(x0, x(z0, z1))))
   A__U12(tt, x(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x(x0, tt)))
   A__U12(tt, x(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x(x0, s(z0))))
   A__U12(tt, x(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x(x0, 0)))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x(U11(z0, z1, z2), x1)))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x(U12(z0, z1, z2), x1)))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x(plus(z0, z1), x1)))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x(U21(z0, z1, z2), x1)))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x(U22(z0, z1, z2), x1)))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x(x(z0, z1), x1)))
   A__U12(tt, x(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x(tt, x1)))
   A__U12(tt, x(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x(s(z0), x1)))
   A__U12(tt, x(0, x1), x2) -> c3(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x(0, x1)))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), tt) -> c3(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x2) -> c3(MARK(x(x0, x1)))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0), MARK(0))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

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

(238)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
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   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
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   A__U12(tt, x(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x2) -> c3(MARK(x(x0, x1)))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(239) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, x0, U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), mark(x0)), MARK(x0)) by 
   A__U12(tt, U11(z0, z1, z2), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, tt, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), tt), MARK(tt))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(0))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0))

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

(240)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
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   A__U12(tt, U22(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U22(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U22(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U22(x(z0, z1), x1, x2)))
   A__U12(tt, U22(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(U22(tt, x1, x2)))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(U22(s(z0), x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c3(MARK(U22(x0, z1, z2)))
   A__U12(tt, U22(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(0, x1, x2)))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x(x0, U11(z0, z1, z2))))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x(x0, U12(z0, z1, z2))))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x(x0, plus(z0, z1))))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x(x0, U21(z0, z1, z2))))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x(x0, U22(z0, z1, z2))))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x(x0, x(z0, z1))))
   A__U12(tt, x(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x(x0, tt)))
   A__U12(tt, x(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x(x0, s(z0))))
   A__U12(tt, x(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x(x0, 0)))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x(U11(z0, z1, z2), x1)))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x(U12(z0, z1, z2), x1)))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x(plus(z0, z1), x1)))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x(U21(z0, z1, z2), x1)))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x(U22(z0, z1, z2), x1)))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x(x(z0, z1), x1)))
   A__U12(tt, x(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x(tt, x1)))
   A__U12(tt, x(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x(s(z0), x1)))
   A__U12(tt, x(0, x1), x2) -> c3(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x(0, x1)))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), tt) -> c3(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x2) -> c3(MARK(x(x0, x1)))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0))
   A__U12(tt, tt, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), tt), MARK(tt))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(0))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
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   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
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   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
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   A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1)))
   A__U12(tt, U21(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U21(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U21(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2)))
   A__U12(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U21(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U21(x(z0, z1), x1, x2)))
   A__U12(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2)))
   A__U12(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2)))
   A__U12(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)))
   A__U12(tt, U22(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U22(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U22(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U22(plus(z0, z1), x1, x2)))
   A__U12(tt, U22(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U22(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U22(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U22(x(z0, z1), x1, x2)))
   A__U12(tt, U22(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(U22(tt, x1, x2)))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(U22(s(z0), x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c3(MARK(U22(x0, z1, z2)))
   A__U12(tt, U22(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(0, x1, x2)))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x(x0, U11(z0, z1, z2))))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x(x0, U12(z0, z1, z2))))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x(x0, plus(z0, z1))))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x(x0, U21(z0, z1, z2))))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x(x0, U22(z0, z1, z2))))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x(x0, x(z0, z1))))
   A__U12(tt, x(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x(x0, tt)))
   A__U12(tt, x(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x(x0, s(z0))))
   A__U12(tt, x(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x(x0, 0)))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x(U11(z0, z1, z2), x1)))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x(U12(z0, z1, z2), x1)))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x(plus(z0, z1), x1)))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x(U21(z0, z1, z2), x1)))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x(U22(z0, z1, z2), x1)))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x(x(z0, z1), x1)))
   A__U12(tt, x(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x(tt, x1)))
   A__U12(tt, x(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x(s(z0), x1)))
   A__U12(tt, x(0, x1), x2) -> c3(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x(0, x1)))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), tt) -> c3(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x2) -> c3(MARK(x(x0, x1)))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0))
   A__U12(tt, tt, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), tt), MARK(tt))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(0))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(241) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   A__U12(tt, tt, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), tt), MARK(tt))

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

(242)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
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   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
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   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
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   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(0))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
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   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x(U11(z0, z1, z2), x1)))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x(U12(z0, z1, z2), x1)))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x(plus(z0, z1), x1)))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x(U21(z0, z1, z2), x1)))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x(U22(z0, z1, z2), x1)))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x(x(z0, z1), x1)))
   A__U12(tt, x(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x(tt, x1)))
   A__U12(tt, x(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x(s(z0), x1)))
   A__U12(tt, x(0, x1), x2) -> c3(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x(0, x1)))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), tt) -> c3(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x2) -> c3(MARK(x(x0, x1)))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0), MARK(0))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

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

(244)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
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   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2)))
   A__U12(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)))
   A__U12(tt, U22(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U22(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U22(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U22(plus(z0, z1), x1, x2)))
   A__U12(tt, U22(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U22(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U22(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U22(x(z0, z1), x1, x2)))
   A__U12(tt, U22(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(U22(tt, x1, x2)))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(U22(s(z0), x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c3(MARK(U22(x0, z1, z2)))
   A__U12(tt, U22(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(0, x1, x2)))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x(x0, U11(z0, z1, z2))))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x(x0, U12(z0, z1, z2))))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x(x0, plus(z0, z1))))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x(x0, U21(z0, z1, z2))))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x(x0, U22(z0, z1, z2))))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x(x0, x(z0, z1))))
   A__U12(tt, x(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x(x0, tt)))
   A__U12(tt, x(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x(x0, s(z0))))
   A__U12(tt, x(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x(x0, 0)))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x(U11(z0, z1, z2), x1)))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x(U12(z0, z1, z2), x1)))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x(plus(z0, z1), x1)))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x(U21(z0, z1, z2), x1)))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x(U22(z0, z1, z2), x1)))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x(x(z0, z1), x1)))
   A__U12(tt, x(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x(tt, x1)))
   A__U12(tt, x(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x(s(z0), x1)))
   A__U12(tt, x(0, x1), x2) -> c3(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x(0, x1)))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), tt) -> c3(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x2) -> c3(MARK(x(x0, x1)))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
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   A__U12(tt, plus(0, x1), x2) -> c3(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U12(tt, plus(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), tt) -> c3(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), 0) -> c3(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U12(tt, plus(x0, x1), x2) -> c3(MARK(plus(x0, x1)))
   A__U12(tt, U21(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U21(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U21(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2)))
   A__U12(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U21(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U21(x(z0, z1), x1, x2)))
   A__U12(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2)))
   A__U12(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2)))
   A__U12(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)))
   A__U12(tt, U22(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U22(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U22(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U22(plus(z0, z1), x1, x2)))
   A__U12(tt, U22(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U22(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U22(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U22(x(z0, z1), x1, x2)))
   A__U12(tt, U22(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(U22(tt, x1, x2)))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(U22(s(z0), x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c3(MARK(U22(x0, z1, z2)))
   A__U12(tt, U22(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(0, x1, x2)))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x(x0, U11(z0, z1, z2))))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x(x0, U12(z0, z1, z2))))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x(x0, plus(z0, z1))))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x(x0, U21(z0, z1, z2))))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x(x0, U22(z0, z1, z2))))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x(x0, x(z0, z1))))
   A__U12(tt, x(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x(x0, tt)))
   A__U12(tt, x(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x(x0, s(z0))))
   A__U12(tt, x(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x(x0, 0)))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x(U11(z0, z1, z2), x1)))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x(U12(z0, z1, z2), x1)))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x(plus(z0, z1), x1)))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x(U21(z0, z1, z2), x1)))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x(U22(z0, z1, z2), x1)))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x(x(z0, z1), x1)))
   A__U12(tt, x(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x(tt, x1)))
   A__U12(tt, x(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x(s(z0), x1)))
   A__U12(tt, x(0, x1), x2) -> c3(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x(0, x1)))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), tt) -> c3(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x2) -> c3(MARK(x(x0, x1)))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(245) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, x0, plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) by 
   A__U12(tt, U11(z0, z1, z2), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, tt, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(tt))
   A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(0))
   A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0))

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

(246)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
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   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
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   A__U12(tt, U22(x0, z1, z2), x3) -> c3(MARK(U22(x0, z1, z2)))
   A__U12(tt, U22(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(0, x1, x2)))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x(x0, U11(z0, z1, z2))))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x(x0, U12(z0, z1, z2))))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x(x0, plus(z0, z1))))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x(x0, U21(z0, z1, z2))))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x(x0, U22(z0, z1, z2))))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x(x0, x(z0, z1))))
   A__U12(tt, x(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x(x0, tt)))
   A__U12(tt, x(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x(x0, s(z0))))
   A__U12(tt, x(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x(x0, 0)))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x(U11(z0, z1, z2), x1)))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x(U12(z0, z1, z2), x1)))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x(plus(z0, z1), x1)))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x(U21(z0, z1, z2), x1)))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x(U22(z0, z1, z2), x1)))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x(x(z0, z1), x1)))
   A__U12(tt, x(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x(tt, x1)))
   A__U12(tt, x(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x(s(z0), x1)))
   A__U12(tt, x(0, x1), x2) -> c3(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x(0, x1)))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), tt) -> c3(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x2) -> c3(MARK(x(x0, x1)))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0))
   A__U12(tt, tt, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(tt))
   A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(0))
   A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
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   A__U12(tt, U21(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U21(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U21(plus(z0, z1), x1, x2)))
   A__U12(tt, U21(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U21(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U21(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U21(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U21(x(z0, z1), x1, x2)))
   A__U12(tt, U21(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(tt, x1, x2)), MARK(U21(tt, x1, x2)))
   A__U12(tt, U21(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(s(mark(z0)), x1, x2)), MARK(U21(s(z0), x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2)))
   A__U12(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)))
   A__U12(tt, U22(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U22(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U22(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U22(plus(z0, z1), x1, x2)))
   A__U12(tt, U22(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U22(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U22(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U22(x(z0, z1), x1, x2)))
   A__U12(tt, U22(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(U22(tt, x1, x2)))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(U22(s(z0), x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c3(MARK(U22(x0, z1, z2)))
   A__U12(tt, U22(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(0, x1, x2)))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x(x0, U11(z0, z1, z2))))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x(x0, U12(z0, z1, z2))))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x(x0, plus(z0, z1))))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x(x0, U21(z0, z1, z2))))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x(x0, U22(z0, z1, z2))))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x(x0, x(z0, z1))))
   A__U12(tt, x(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x(x0, tt)))
   A__U12(tt, x(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x(x0, s(z0))))
   A__U12(tt, x(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x(x0, 0)))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x(U11(z0, z1, z2), x1)))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x(U12(z0, z1, z2), x1)))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x(plus(z0, z1), x1)))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x(U21(z0, z1, z2), x1)))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x(U22(z0, z1, z2), x1)))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x(x(z0, z1), x1)))
   A__U12(tt, x(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x(tt, x1)))
   A__U12(tt, x(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x(s(z0), x1)))
   A__U12(tt, x(0, x1), x2) -> c3(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x(0, x1)))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), tt) -> c3(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x2) -> c3(MARK(x(x0, x1)))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0))
   A__U12(tt, tt, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(tt))
   A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(0))
   A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(247) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   A__U12(tt, tt, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(tt))

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

(248)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
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   A__U12(tt, x(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x(s(z0), x1)))
   A__U12(tt, x(0, x1), x2) -> c3(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x(0, x1)))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), tt) -> c3(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x2) -> c3(MARK(x(x0, x1)))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(0))
   A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
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   A__U12(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2)))
   A__U12(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)))
   A__U12(tt, U22(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U22(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U22(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U22(plus(z0, z1), x1, x2)))
   A__U12(tt, U22(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U22(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U22(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U22(x(z0, z1), x1, x2)))
   A__U12(tt, U22(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(U22(tt, x1, x2)))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(U22(s(z0), x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c3(MARK(U22(x0, z1, z2)))
   A__U12(tt, U22(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(0, x1, x2)))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x(x0, U11(z0, z1, z2))))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x(x0, U12(z0, z1, z2))))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x(x0, plus(z0, z1))))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x(x0, U21(z0, z1, z2))))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x(x0, U22(z0, z1, z2))))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x(x0, x(z0, z1))))
   A__U12(tt, x(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x(x0, tt)))
   A__U12(tt, x(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x(x0, s(z0))))
   A__U12(tt, x(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x(x0, 0)))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x(U11(z0, z1, z2), x1)))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x(U12(z0, z1, z2), x1)))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x(plus(z0, z1), x1)))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x(U21(z0, z1, z2), x1)))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x(U22(z0, z1, z2), x1)))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x(x(z0, z1), x1)))
   A__U12(tt, x(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x(tt, x1)))
   A__U12(tt, x(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x(s(z0), x1)))
   A__U12(tt, x(0, x1), x2) -> c3(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x(0, x1)))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), tt) -> c3(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x2) -> c3(MARK(x(x0, x1)))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(0))
   A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

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

(250)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
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   A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
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   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
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   A__U12(tt, U22(x0, z1, z2), x3) -> c3(MARK(U22(x0, z1, z2)))
   A__U12(tt, U22(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(0, x1, x2)))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x(x0, U11(z0, z1, z2))))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x(x0, U12(z0, z1, z2))))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x(x0, plus(z0, z1))))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x(x0, U21(z0, z1, z2))))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x(x0, U22(z0, z1, z2))))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x(x0, x(z0, z1))))
   A__U12(tt, x(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x(x0, tt)))
   A__U12(tt, x(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x(x0, s(z0))))
   A__U12(tt, x(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x(x0, 0)))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x(U11(z0, z1, z2), x1)))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x(U12(z0, z1, z2), x1)))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x(plus(z0, z1), x1)))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x(U21(z0, z1, z2), x1)))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x(U22(z0, z1, z2), x1)))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x(x(z0, z1), x1)))
   A__U12(tt, x(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x(tt, x1)))
   A__U12(tt, x(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x(s(z0), x1)))
   A__U12(tt, x(0, x1), x2) -> c3(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x(0, x1)))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), tt) -> c3(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x2) -> c3(MARK(x(x0, x1)))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(251) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, x0, U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), mark(x0)), MARK(x0)) by 
   A__U12(tt, U11(z0, z1, z2), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, tt, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), tt), MARK(tt))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(0))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0))

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

(252)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
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   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U12(U21(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U12(U22(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c19(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, U21(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U21(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U22(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U22(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, x(z0, z1))) -> c19(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
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   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0))
   A__U12(tt, tt, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), tt), MARK(tt))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(0))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
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   A__U12(tt, U22(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U22(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U22(x(z0, z1), x1, x2)))
   A__U12(tt, U22(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(U22(tt, x1, x2)))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(U22(s(z0), x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c3(MARK(U22(x0, z1, z2)))
   A__U12(tt, U22(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(0, x1, x2)))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x(x0, U11(z0, z1, z2))))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x(x0, U12(z0, z1, z2))))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x(x0, plus(z0, z1))))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x(x0, U21(z0, z1, z2))))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x(x0, U22(z0, z1, z2))))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x(x0, x(z0, z1))))
   A__U12(tt, x(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x(x0, tt)))
   A__U12(tt, x(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x(x0, s(z0))))
   A__U12(tt, x(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x(x0, 0)))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x(U11(z0, z1, z2), x1)))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x(U12(z0, z1, z2), x1)))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x(plus(z0, z1), x1)))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x(U21(z0, z1, z2), x1)))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x(U22(z0, z1, z2), x1)))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x(x(z0, z1), x1)))
   A__U12(tt, x(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x(tt, x1)))
   A__U12(tt, x(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x(s(z0), x1)))
   A__U12(tt, x(0, x1), x2) -> c3(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x(0, x1)))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), tt) -> c3(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x2) -> c3(MARK(x(x0, x1)))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0))
   A__U12(tt, tt, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), tt), MARK(tt))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(0))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(253) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   A__U12(tt, tt, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), tt), MARK(tt))

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

(254)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
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   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(0))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
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   A__U12(tt, U22(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U22(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U22(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U22(plus(z0, z1), x1, x2)))
   A__U12(tt, U22(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U22(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U22(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U22(x(z0, z1), x1, x2)))
   A__U12(tt, U22(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(U22(tt, x1, x2)))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(U22(s(z0), x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c3(MARK(U22(x0, z1, z2)))
   A__U12(tt, U22(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(0, x1, x2)))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x(x0, U11(z0, z1, z2))))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x(x0, U12(z0, z1, z2))))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x(x0, plus(z0, z1))))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x(x0, U21(z0, z1, z2))))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x(x0, U22(z0, z1, z2))))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x(x0, x(z0, z1))))
   A__U12(tt, x(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x(x0, tt)))
   A__U12(tt, x(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x(x0, s(z0))))
   A__U12(tt, x(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x(x0, 0)))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x(U11(z0, z1, z2), x1)))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x(U12(z0, z1, z2), x1)))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x(plus(z0, z1), x1)))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x(U21(z0, z1, z2), x1)))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x(U22(z0, z1, z2), x1)))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x(x(z0, z1), x1)))
   A__U12(tt, x(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x(tt, x1)))
   A__U12(tt, x(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x(s(z0), x1)))
   A__U12(tt, x(0, x1), x2) -> c3(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x(0, x1)))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), tt) -> c3(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x2) -> c3(MARK(x(x0, x1)))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0), MARK(0))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

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

(256)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
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   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x2) -> c3(MARK(x(x0, x1)))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
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   A__U12(tt, U21(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U21(mark(x0), x1, x2)), MARK(U21(x0, x1, x2)))
   A__U12(tt, U21(x0, z1, z2), x3) -> c3(MARK(U21(x0, z1, z2)))
   A__U12(tt, U21(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U21(0, x1, x2)))
   A__U12(tt, U22(U11(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U11(mark(z0), z1, z2), x1, x2)), MARK(U22(U11(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U12(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U12(mark(z0), z1, z2), x1, x2)), MARK(U22(U12(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(plus(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U22(plus(z0, z1), x1, x2)))
   A__U12(tt, U22(U21(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U21(mark(z0), z1, z2), x1, x2)), MARK(U22(U21(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(U22(z0, z1, z2), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__U22(mark(z0), z1, z2), x1, x2)), MARK(U22(U22(z0, z1, z2), x1, x2)))
   A__U12(tt, U22(x(z0, z1), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(a__x(mark(z0), mark(z1)), x1, x2)), MARK(U22(x(z0, z1), x1, x2)))
   A__U12(tt, U22(tt, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(tt, x1, x2)), MARK(U22(tt, x1, x2)))
   A__U12(tt, U22(s(z0), x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(s(mark(z0)), x1, x2)), MARK(U22(s(z0), x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), tt) -> c3(A__PLUS(tt, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, x1, x2), 0) -> c3(A__PLUS(0, a__U22(mark(x0), x1, x2)), MARK(U22(x0, x1, x2)))
   A__U12(tt, U22(x0, z1, z2), x3) -> c3(MARK(U22(x0, z1, z2)))
   A__U12(tt, U22(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(0, x1, x2)))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x(x0, U11(z0, z1, z2))))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x(x0, U12(z0, z1, z2))))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x(x0, plus(z0, z1))))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x(x0, U21(z0, z1, z2))))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x(x0, U22(z0, z1, z2))))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x(x0, x(z0, z1))))
   A__U12(tt, x(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x(x0, tt)))
   A__U12(tt, x(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x(x0, s(z0))))
   A__U12(tt, x(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x(x0, 0)))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x(U11(z0, z1, z2), x1)))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x(U12(z0, z1, z2), x1)))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x(plus(z0, z1), x1)))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x(U21(z0, z1, z2), x1)))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x(U22(z0, z1, z2), x1)))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x(x(z0, z1), x1)))
   A__U12(tt, x(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x(tt, x1)))
   A__U12(tt, x(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x(s(z0), x1)))
   A__U12(tt, x(0, x1), x2) -> c3(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x(0, x1)))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), tt) -> c3(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x2) -> c3(MARK(x(x0, x1)))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(257) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, x0, U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), mark(x0)), MARK(x0)) by 
   A__U12(tt, U11(z0, z1, z2), U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, tt, U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), tt), MARK(tt))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), 0), MARK(0))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c3(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c3(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c3(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(0, x2, x3)) -> c3(A__PLUS(a__U22(0, x2, x3), mark(x0)), MARK(x0))

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

(258)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
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   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x(x0, U11(z0, z1, z2))))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x(x0, U12(z0, z1, z2))))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x(x0, plus(z0, z1))))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x(x0, U21(z0, z1, z2))))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x(x0, U22(z0, z1, z2))))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x(x0, x(z0, z1))))
   A__U12(tt, x(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x(x0, tt)))
   A__U12(tt, x(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x(x0, s(z0))))
   A__U12(tt, x(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x(x0, 0)))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x(U11(z0, z1, z2), x1)))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x(U12(z0, z1, z2), x1)))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x(plus(z0, z1), x1)))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x(U21(z0, z1, z2), x1)))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x(U22(z0, z1, z2), x1)))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x(x(z0, z1), x1)))
   A__U12(tt, x(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x(tt, x1)))
   A__U12(tt, x(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x(s(z0), x1)))
   A__U12(tt, x(0, x1), x2) -> c3(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x(0, x1)))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), tt) -> c3(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x2) -> c3(MARK(x(x0, x1)))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0))
   A__U12(tt, tt, U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), tt), MARK(tt))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), 0), MARK(0))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c3(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c3(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c3(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(0, x2, x3)) -> c3(A__PLUS(a__U22(0, x2, x3), mark(x0)), MARK(x0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
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   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
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   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
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   A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0))
   A__U12(tt, tt, U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), tt), MARK(tt))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), 0), MARK(0))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c3(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c3(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c3(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(0, x2, x3)) -> c3(A__PLUS(a__U22(0, x2, x3), mark(x0)), MARK(x0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(259) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   A__U12(tt, tt, U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), tt), MARK(tt))

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

(260)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
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   A__U12(tt, x0, U22(x1, z1, z2)) -> c3(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c3(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c3(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(0, x2, x3)) -> c3(A__PLUS(a__U22(0, x2, x3), mark(x0)), MARK(x0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
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   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), tt) -> c3(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x2) -> c3(MARK(x(x0, x1)))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), 0), MARK(0))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c3(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c3(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c3(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(0, x2, x3)) -> c3(A__PLUS(a__U22(0, x2, x3), mark(x0)), MARK(x0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

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

(262)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
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   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c3(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c3(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c3(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(0, x2, x3)) -> c3(A__PLUS(a__U22(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), 0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
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   A__U12(tt, plus(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
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   A__U12(tt, U22(x0, z1, z2), x3) -> c3(MARK(U22(x0, z1, z2)))
   A__U12(tt, U22(0, x1, x2), x3) -> c3(A__PLUS(mark(x3), a__U22(0, x1, x2)))
   A__U12(tt, x(x0, U11(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U11(mark(z0), z1, z2))), MARK(x(x0, U11(z0, z1, z2))))
   A__U12(tt, x(x0, U12(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U12(mark(z0), z1, z2))), MARK(x(x0, U12(z0, z1, z2))))
   A__U12(tt, x(x0, plus(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x(x0, plus(z0, z1))))
   A__U12(tt, x(x0, U21(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U21(mark(z0), z1, z2))), MARK(x(x0, U21(z0, z1, z2))))
   A__U12(tt, x(x0, U22(z0, z1, z2)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__U22(mark(z0), z1, z2))), MARK(x(x0, U22(z0, z1, z2))))
   A__U12(tt, x(x0, x(z0, z1)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), a__x(mark(z0), mark(z1)))), MARK(x(x0, x(z0, z1))))
   A__U12(tt, x(x0, tt), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), tt)), MARK(x(x0, tt)))
   A__U12(tt, x(x0, s(z0)), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), s(mark(z0)))), MARK(x(x0, s(z0))))
   A__U12(tt, x(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x(x0, 0)))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x(U11(z0, z1, z2), x1)))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x(U12(z0, z1, z2), x1)))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x(plus(z0, z1), x1)))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x(U21(z0, z1, z2), x1)))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x(U22(z0, z1, z2), x1)))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x(x(z0, z1), x1)))
   A__U12(tt, x(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x(tt, x1)))
   A__U12(tt, x(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x(s(z0), x1)))
   A__U12(tt, x(0, x1), x2) -> c3(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x(0, x1)))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), tt) -> c3(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x2) -> c3(MARK(x(x0, x1)))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c3(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c3(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c3(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(0, x2, x3)) -> c3(A__PLUS(a__U22(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), 0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(263) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U12(tt, x0, x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) by 
   A__U12(tt, U11(z0, z1, z2), x(x1, x2)) -> c3(A__PLUS(a__x(mark(x1), mark(x2)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U12(tt, U12(z0, z1, z2), x(x1, x2)) -> c3(A__PLUS(a__x(mark(x1), mark(x2)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U12(tt, plus(z0, z1), x(x1, x2)) -> c3(A__PLUS(a__x(mark(x1), mark(x2)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U12(tt, U21(z0, z1, z2), x(x1, x2)) -> c3(A__PLUS(a__x(mark(x1), mark(x2)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U12(tt, U22(z0, z1, z2), x(x1, x2)) -> c3(A__PLUS(a__x(mark(x1), mark(x2)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U12(tt, x(z0, z1), x(x1, x2)) -> c3(A__PLUS(a__x(mark(x1), mark(x2)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U12(tt, tt, x(x1, x2)) -> c3(A__PLUS(a__x(mark(x1), mark(x2)), tt), MARK(tt))
   A__U12(tt, s(z0), x(x1, x2)) -> c3(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, x(x1, x2)) -> c3(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(0))
   A__U12(tt, x0, x(x1, x2)) -> c3(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, plus(z0, z1))) -> c3(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, U22(z0, z1, z2))) -> c3(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, x(z0, z1))) -> c3(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, tt)) -> c3(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, s(z0))) -> c3(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, 0)) -> c3(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(tt, x2)) -> c3(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(s(z0), x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(0, x2)) -> c3(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x0))

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

(264)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
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   A__U12(tt, x(x0, 0), x2) -> c3(A__PLUS(mark(x2), a__x(mark(x0), 0)), MARK(x(x0, 0)))
   A__U12(tt, x(U11(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U11(mark(z0), z1, z2), mark(x1))), MARK(x(U11(z0, z1, z2), x1)))
   A__U12(tt, x(U12(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U12(mark(z0), z1, z2), mark(x1))), MARK(x(U12(z0, z1, z2), x1)))
   A__U12(tt, x(plus(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x(plus(z0, z1), x1)))
   A__U12(tt, x(U21(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U21(mark(z0), z1, z2), mark(x1))), MARK(x(U21(z0, z1, z2), x1)))
   A__U12(tt, x(U22(z0, z1, z2), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__U22(mark(z0), z1, z2), mark(x1))), MARK(x(U22(z0, z1, z2), x1)))
   A__U12(tt, x(x(z0, z1), x1), x2) -> c3(A__PLUS(mark(x2), a__x(a__x(mark(z0), mark(z1)), mark(x1))), MARK(x(x(z0, z1), x1)))
   A__U12(tt, x(tt, x1), x2) -> c3(A__PLUS(mark(x2), a__x(tt, mark(x1))), MARK(x(tt, x1)))
   A__U12(tt, x(s(z0), x1), x2) -> c3(A__PLUS(mark(x2), a__x(s(mark(z0)), mark(x1))), MARK(x(s(z0), x1)))
   A__U12(tt, x(0, x1), x2) -> c3(A__PLUS(mark(x2), a__x(0, mark(x1))), MARK(x(0, x1)))
   A__U12(tt, x(x0, x1), U11(z0, z1, z2)) -> c3(A__PLUS(a__U11(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U12(z0, z1, z2)) -> c3(A__PLUS(a__U12(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), plus(z0, z1)) -> c3(A__PLUS(a__plus(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U21(z0, z1, z2)) -> c3(A__PLUS(a__U21(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), U22(z0, z1, z2)) -> c3(A__PLUS(a__U22(mark(z0), z1, z2), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), tt) -> c3(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x2) -> c3(MARK(x(x0, x1)))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c3(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c3(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c3(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(0, x2, x3)) -> c3(A__PLUS(a__U22(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), 0))
   A__U12(tt, tt, x(x1, x2)) -> c3(A__PLUS(a__x(mark(x1), mark(x2)), tt), MARK(tt))
   A__U12(tt, s(z0), x(x1, x2)) -> c3(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, x(x1, x2)) -> c3(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(0))
   A__U12(tt, x0, x(x1, x2)) -> c3(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, plus(z0, z1))) -> c3(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, U22(z0, z1, z2))) -> c3(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, x(z0, z1))) -> c3(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, tt)) -> c3(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, s(z0))) -> c3(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, 0)) -> c3(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(tt, x2)) -> c3(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(s(z0), x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(0, x2)) -> c3(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
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   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
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   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
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   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
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   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
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   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
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   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U11(tt, x1, x2)) -> c17(A__U11(tt, x1, x2))
   MARK(U11(s(z0), x1, x2)) -> c17(MARK(s(z0)))
   MARK(U12(U11(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U12(U12(z0, z1, z2), x1, x2)) -> c18(A__U12(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U12(plus(z0, z1), x1, x2)) -> c18(A__U12(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
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   MARK(U12(x(z0, z1), x1, x2)) -> c18(A__U12(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
   MARK(U12(tt, x1, x2)) -> c18(A__U12(tt, x1, x2))
   MARK(U12(s(z0), x1, x2)) -> c18(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U11(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U12(z0, z1, z2))) -> c19(A__PLUS(mark(x0), a__U12(mark(z0), z1, z2)), MARK(x0))
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   MARK(plus(x0, s(z0))) -> c19(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
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   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c3(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c3(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c3(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(0, x2, x3)) -> c3(A__PLUS(a__U22(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), 0))
   A__U12(tt, tt, x(x1, x2)) -> c3(A__PLUS(a__x(mark(x1), mark(x2)), tt), MARK(tt))
   A__U12(tt, s(z0), x(x1, x2)) -> c3(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, x(x1, x2)) -> c3(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(0))
   A__U12(tt, x0, x(x1, x2)) -> c3(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, plus(z0, z1))) -> c3(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, U22(z0, z1, z2))) -> c3(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, x(z0, z1))) -> c3(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, tt)) -> c3(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, s(z0))) -> c3(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, 0)) -> c3(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(tt, x2)) -> c3(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(s(z0), x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(0, x2)) -> c3(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

(265) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   A__U12(tt, tt, x(x1, x2)) -> c3(A__PLUS(a__x(mark(x1), mark(x2)), tt), MARK(tt))

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

(266)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
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   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c3(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c3(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c3(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(0, x2, x3)) -> c3(A__PLUS(a__U22(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), x(x1, x2)) -> c3(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, x(x1, x2)) -> c3(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(0))
   A__U12(tt, x0, x(x1, x2)) -> c3(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, plus(z0, z1))) -> c3(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, U22(z0, z1, z2))) -> c3(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, x(z0, z1))) -> c3(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, tt)) -> c3(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, s(z0))) -> c3(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, 0)) -> c3(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(tt, x2)) -> c3(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(s(z0), x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(0, x2)) -> c3(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
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   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c3(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c3(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(0, x2, x3)) -> c3(A__PLUS(a__U22(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), x(x1, x2)) -> c3(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, 0, x(x1, x2)) -> c3(A__PLUS(a__x(mark(x1), mark(x2)), 0), MARK(0))
   A__U12(tt, x0, x(x1, x2)) -> c3(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, plus(z0, z1))) -> c3(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, U22(z0, z1, z2))) -> c3(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, x(z0, z1))) -> c3(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, tt)) -> c3(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, s(z0))) -> c3(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, 0)) -> c3(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(tt, x2)) -> c3(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(s(z0), x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(0, x2)) -> c3(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

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

(268)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0, z1) -> a__U12(tt, z0, z1)
   a__U11(z0, z1, z2) -> U11(z0, z1, z2)
   a__U12(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U12(z0, z1, z2) -> U12(z0, z1, z2)
   a__U21(tt, z0, z1) -> a__U22(tt, z0, z1)
   a__U21(z0, z1, z2) -> U21(z0, z1, z2)
   a__U22(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1))
   a__U22(z0, z1, z2) -> U22(z0, z1, z2)
   a__plus(z0, 0) -> mark(z0)
   a__plus(z0, s(z1)) -> a__U11(tt, z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   a__x(z0, 0) -> 0
   a__x(z0, s(z1)) -> a__U21(tt, z1, z0)
   a__x(z0, z1) -> x(z0, z1)
   mark(U11(z0, z1, z2)) -> a__U11(mark(z0), z1, z2)
   mark(U12(z0, z1, z2)) -> a__U12(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(U21(z0, z1, z2)) -> a__U21(mark(z0), z1, z2)
   mark(U22(z0, z1, z2)) -> a__U22(mark(z0), z1, z2)
   mark(x(z0, z1)) -> a__x(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
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   A__U12(tt, x0, x(x1, 0)) -> c3(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(tt, x2)) -> c3(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(s(z0), x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(0, x2)) -> c3(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, 0, x(x1, x2)) -> c3(A__PLUS(a__x(mark(x1), mark(x2)), 0))
S tuples:
   A__U11(tt, z0, z1) -> c(A__U12(tt, z0, z1))
   A__U21(tt, z0, z1) -> c5(A__U22(tt, z0, z1))
   A__PLUS(z0, 0) -> c11(MARK(z0))
   A__PLUS(z0, s(z1)) -> c12(A__U11(tt, z1, z0))
   A__X(z0, s(z1)) -> c15(A__U21(tt, z1, z0))
   MARK(s(z0)) -> c26(MARK(z0))
   A__U12(tt, s(z0), x1) -> c2(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U12(tt, 0, x1) -> c2(A__PLUS(mark(x1), 0), MARK(x1))
   A__U12(tt, tt, x1) -> c2(MARK(x1))
   A__U12(tt, s(z0), x1) -> c3(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, tt) -> c3(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U12(tt, x0, s(z0)) -> c3(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U12(tt, x0, 0) -> c3(A__PLUS(0, mark(x0)), MARK(x0))
   A__U12(tt, 0, x1) -> c3(A__PLUS(mark(x1), 0))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c7(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c7(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c7(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1))
   A__U22(tt, tt, x1) -> c7(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c7(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1))
   A__U22(tt, 0, x1) -> c7(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c7(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c7(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c7(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c7(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0)))
   A__U22(tt, x0, tt) -> c7(A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, tt) -> c7(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)))
   A__U22(tt, x0, 0) -> c7(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, x1) -> c8(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0))
   A__U22(tt, U11(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, U12(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, plus(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, U21(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, U22(z0, z1, z2), x1) -> c8(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x(z0, z1), x1) -> c8(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, s(z0), x1) -> c8(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), A__X(mark(U11(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), A__X(mark(U12(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, plus(z0, z1)) -> c8(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), A__X(mark(U21(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c8(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), A__X(mark(U22(z0, z1, z2)), mark(x0)), MARK(x0))
   A__U22(tt, x0, x(z0, z1)) -> c8(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, x0, s(z0)) -> c8(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0))
   A__U22(tt, x0, 0) -> c8(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0))
   A__U22(tt, x0, tt) -> c8(A__X(mark(tt), mark(x0)), MARK(x0))
   A__U22(tt, tt, x1) -> c8(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)))
   A__U22(tt, 0, x1) -> c8(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U11(z0, z1, z2)), mark(x0)), a__U11(mark(z0), z1, z2)), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U12(z0, z1, z2)), mark(x0)), a__U12(mark(z0), z1, z2)), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U21(z0, z1, z2)), mark(x0)), a__U21(mark(z0), z1, z2)), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(mark(U22(z0, z1, z2)), mark(x0)), a__U22(mark(z0), z1, z2)), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0)))
   A__U22(tt, x0, x1) -> c9(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1))
   A__U22(tt, U11(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U12(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, plus(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, U21(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, U22(z0, z1, z2), x1) -> c9(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x1)), MARK(x1))
   A__U22(tt, x(z0, z1), x1) -> c9(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1))
   A__U22(tt, tt, x1) -> c9(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1))
   A__U22(tt, s(z0), x1) -> c9(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1))
   A__U22(tt, 0, x1) -> c9(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1))
   A__U22(tt, x0, U11(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x0)), mark(U11(z0, z1, z2))), MARK(U11(z0, z1, z2)))
   A__U22(tt, x0, U12(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x0)), mark(U12(z0, z1, z2))), MARK(U12(z0, z1, z2)))
   A__U22(tt, x0, plus(z0, z1)) -> c9(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1)))
   A__U22(tt, x0, U21(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x0)), mark(U21(z0, z1, z2))), MARK(U21(z0, z1, z2)))
   A__U22(tt, x0, U22(z0, z1, z2)) -> c9(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x0)), mark(U22(z0, z1, z2))), MARK(U22(z0, z1, z2)))
   A__U22(tt, x0, x(z0, z1)) -> c9(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1)))
   A__U22(tt, x0, s(z0)) -> c9(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(mark(0), mark(x0)), 0))
   A__U22(tt, x0, tt) -> c9(A__PLUS(a__x(tt, mark(x0)), mark(tt)))
   A__U22(tt, x0, 0) -> c9(A__PLUS(a__x(0, mark(x0)), mark(0)))
   MARK(U11(U11(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U11(mark(z0), z1, z2), x1, x2), MARK(U11(z0, z1, z2)))
   MARK(U11(U12(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U12(mark(z0), z1, z2), x1, x2), MARK(U12(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1, x2)) -> c17(A__U11(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U11(U21(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U21(mark(z0), z1, z2), x1, x2), MARK(U21(z0, z1, z2)))
   MARK(U11(U22(z0, z1, z2), x1, x2)) -> c17(A__U11(a__U22(mark(z0), z1, z2), x1, x2), MARK(U22(z0, z1, z2)))
   MARK(U11(x(z0, z1), x1, x2)) -> c17(A__U11(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1)))
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   A__U12(tt, x(x0, x1), x(z0, z1)) -> c3(A__PLUS(a__x(mark(z0), mark(z1)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), tt) -> c3(A__PLUS(tt, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), s(z0)) -> c3(A__PLUS(s(mark(z0)), a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), 0) -> c3(A__PLUS(0, a__x(mark(x0), mark(x1))), MARK(x(x0, x1)))
   A__U12(tt, x(x0, x1), x2) -> c3(MARK(x(x0, x1)))
   A__U12(tt, s(z0), U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U11(x1, z1, z2)) -> c3(A__PLUS(U11(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U11(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U11(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(tt, x2, x3)) -> c3(A__PLUS(a__U11(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(s(z0), x2, x3)) -> c3(A__PLUS(a__U11(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U11(0, x2, x3)) -> c3(A__PLUS(a__U11(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U11(x1, x2, x3)) -> c3(A__PLUS(a__U11(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U12(x1, z1, z2)) -> c3(A__PLUS(U12(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U12(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U12(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(tt, x2, x3)) -> c3(A__PLUS(a__U12(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(s(z0), x2, x3)) -> c3(A__PLUS(a__U12(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U12(0, x2, x3)) -> c3(A__PLUS(a__U12(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U12(x1, x2, x3)) -> c3(A__PLUS(a__U12(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, plus(x1, x2)) -> c3(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, plus(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, U22(z0, z1, z2))) -> c3(A__PLUS(a__plus(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, x(z0, z1))) -> c3(A__PLUS(a__plus(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, tt)) -> c3(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, s(z0))) -> c3(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x1, 0)) -> c3(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(plus(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__plus(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(x(z0, z1), x2)) -> c3(A__PLUS(a__plus(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(tt, x2)) -> c3(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(s(z0), x2)) -> c3(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, plus(0, x2)) -> c3(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, 0, plus(x1, x2)) -> c3(A__PLUS(a__plus(mark(x1), mark(x2)), 0))
   A__U12(tt, s(z0), U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U21(x1, z1, z2)) -> c3(A__PLUS(U21(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U21(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U21(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(tt, x2, x3)) -> c3(A__PLUS(a__U21(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(s(z0), x2, x3)) -> c3(A__PLUS(a__U21(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U21(0, x2, x3)) -> c3(A__PLUS(a__U21(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U21(x1, x2, x3)) -> c3(A__PLUS(a__U21(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, U22(x1, z1, z2)) -> c3(A__PLUS(U22(mark(x1), z1, z2), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U11(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U11(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U12(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U12(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(plus(z0, z1), x2, x3)) -> c3(A__PLUS(a__U22(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U21(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U21(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(U22(z0, z1, z2), x2, x3)) -> c3(A__PLUS(a__U22(a__U22(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(x(z0, z1), x2, x3)) -> c3(A__PLUS(a__U22(a__x(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(tt, x2, x3)) -> c3(A__PLUS(a__U22(tt, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(s(z0), x2, x3)) -> c3(A__PLUS(a__U22(s(mark(z0)), x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, x0, U22(0, x2, x3)) -> c3(A__PLUS(a__U22(0, x2, x3), mark(x0)), MARK(x0))
   A__U12(tt, 0, U22(x1, x2, x3)) -> c3(A__PLUS(a__U22(mark(x1), x2, x3), 0))
   A__U12(tt, s(z0), x(x1, x2)) -> c3(A__PLUS(a__x(mark(x1), mark(x2)), s(mark(z0))), MARK(s(z0)))
   A__U12(tt, x0, x(x1, x2)) -> c3(A__PLUS(x(mark(x1), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, U11(z0, z1, z2))) -> c3(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, U12(z0, z1, z2))) -> c3(A__PLUS(a__x(mark(x1), a__U12(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, plus(z0, z1))) -> c3(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, U21(z0, z1, z2))) -> c3(A__PLUS(a__x(mark(x1), a__U21(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, U22(z0, z1, z2))) -> c3(A__PLUS(a__x(mark(x1), a__U22(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, x(z0, z1))) -> c3(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, tt)) -> c3(A__PLUS(a__x(mark(x1), tt), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, s(z0))) -> c3(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x1, 0)) -> c3(A__PLUS(a__x(mark(x1), 0), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(U11(z0, z1, z2), x2)) -> c3(A__PLUS(a__x(a__U11(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(U12(z0, z1, z2), x2)) -> c3(A__PLUS(a__x(a__U12(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(plus(z0, z1), x2)) -> c3(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(U21(z0, z1, z2), x2)) -> c3(A__PLUS(a__x(a__U21(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(U22(z0, z1, z2), x2)) -> c3(A__PLUS(a__x(a__U22(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(x(z0, z1), x2)) -> c3(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(tt, x2)) -> c3(A__PLUS(a__x(tt, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(s(z0), x2)) -> c3(A__PLUS(a__x(s(mark(z0)), mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, x0, x(0, x2)) -> c3(A__PLUS(a__x(0, mark(x2)), mark(x0)), MARK(x0))
   A__U12(tt, 0, x(x1, x2)) -> c3(A__PLUS(a__x(mark(x1), mark(x2)), 0))
K tuples:none
Defined Rule Symbols:   a__U11_3, a__U12_3, a__U21_3, a__U22_3, a__plus_2, a__x_2, mark_1

Defined Pair Symbols:   A__U11_3, A__U21_3, A__PLUS_2, A__X_2, MARK_1, A__U12_3, A__U22_3

Compound Symbols:   c_1, c5_1, c11_1, c12_1, c15_1, c26_1, c2_2, c2_1, c3_2, c3_1, c7_3, c7_1, c7_2, c8_3, c8_2, c9_2, c9_1, c17_2, c17_1, c18_2, c18_1, c19_2, c19_1, c20_2, c20_1, c21_2, c21_1, c22_2, c22_1, c23_2, c23_1, c24_2


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

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

(270)
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, M, N) -> a__U12(tt, M, N) [1]
   a__U12(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1]
   a__U21(tt, M, N) -> a__U22(tt, M, N) [1]
   a__U22(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)) [1]
   a__plus(N, 0) -> mark(N) [1]
   a__plus(N, s(M)) -> a__U11(tt, M, N) [1]
   a__x(N, 0) -> 0 [1]
   a__x(N, s(M)) -> a__U21(tt, M, N) [1]
   mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) [1]
   mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) [1]
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1]
   mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) [1]
   mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3) [1]
   mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) [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, X3) -> U12(X1, X2, X3) [1]
   a__plus(X1, X2) -> plus(X1, X2) [1]
   a__U21(X1, X2, X3) -> U21(X1, X2, X3) [1]
   a__U22(X1, X2, X3) -> U22(X1, X2, X3) [1]
   a__x(X1, X2) -> x(X1, X2) [1]

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

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

(272)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   a__U11(tt, M, N) -> a__U12(tt, M, N) [1]
   a__U12(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1]
   a__U21(tt, M, N) -> a__U22(tt, M, N) [1]
   a__U22(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)) [1]
   a__plus(N, 0) -> mark(N) [1]
   a__plus(N, s(M)) -> a__U11(tt, M, N) [1]
   a__x(N, 0) -> 0 [1]
   a__x(N, s(M)) -> a__U21(tt, M, N) [1]
   mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) [1]
   mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) [1]
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1]
   mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) [1]
   mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3) [1]
   mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) [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, X3) -> U12(X1, X2, X3) [1]
   a__plus(X1, X2) -> plus(X1, X2) [1]
   a__U21(X1, X2, X3) -> U21(X1, X2, X3) [1]
   a__U22(X1, X2, X3) -> U22(X1, X2, X3) [1]
   a__x(X1, X2) -> x(X1, X2) [1]

The TRS has the following type information:
a__U11 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
tt :: tt:s:0:U11:U12:plus:U21:U22:x
a__U12 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
s :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
a__plus :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
mark :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
a__U21 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
a__U22 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
a__x :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
0 :: tt:s:0:U11:U12:plus:U21:U22:x
U11 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
U12 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
plus :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
U21 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
U22 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
x :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x

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

(273) 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__x_2
   a__U22_3
   a__U12_3
   a__U21_3
   a__plus_2
   a__U11_3

Due to the following rules being added:
none

And the following fresh constants: none

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

(274)
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, M, N) -> a__U12(tt, M, N) [1]
   a__U12(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1]
   a__U21(tt, M, N) -> a__U22(tt, M, N) [1]
   a__U22(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)) [1]
   a__plus(N, 0) -> mark(N) [1]
   a__plus(N, s(M)) -> a__U11(tt, M, N) [1]
   a__x(N, 0) -> 0 [1]
   a__x(N, s(M)) -> a__U21(tt, M, N) [1]
   mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) [1]
   mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) [1]
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1]
   mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) [1]
   mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3) [1]
   mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) [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, X3) -> U12(X1, X2, X3) [1]
   a__plus(X1, X2) -> plus(X1, X2) [1]
   a__U21(X1, X2, X3) -> U21(X1, X2, X3) [1]
   a__U22(X1, X2, X3) -> U22(X1, X2, X3) [1]
   a__x(X1, X2) -> x(X1, X2) [1]

The TRS has the following type information:
a__U11 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
tt :: tt:s:0:U11:U12:plus:U21:U22:x
a__U12 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
s :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
a__plus :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
mark :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
a__U21 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
a__U22 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
a__x :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
0 :: tt:s:0:U11:U12:plus:U21:U22:x
U11 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
U12 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
plus :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
U21 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
U22 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
x :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x

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

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

(276)
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, M, N) -> a__U12(tt, M, N) [1]
   a__U12(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1]
   a__U21(tt, M, N) -> a__U22(tt, M, N) [1]
   a__U22(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)) [1]
   a__plus(N, 0) -> mark(N) [1]
   a__plus(N, s(M)) -> a__U11(tt, M, N) [1]
   a__x(N, 0) -> 0 [1]
   a__x(N, s(M)) -> a__U21(tt, M, N) [1]
   mark(U11(U11(X1119, X2119, X379), X2, X3)) -> a__U11(a__U11(mark(X1119), X2119, X379), X2, X3) [2]
   mark(U11(U12(X1120, X2120, X380), X2, X3)) -> a__U11(a__U12(mark(X1120), X2120, X380), X2, X3) [2]
   mark(U11(plus(X1121, X2121), X2, X3)) -> a__U11(a__plus(mark(X1121), mark(X2121)), X2, X3) [2]
   mark(U11(U21(X1122, X2122, X381), X2, X3)) -> a__U11(a__U21(mark(X1122), X2122, X381), X2, X3) [2]
   mark(U11(U22(X1123, X2123, X382), X2, X3)) -> a__U11(a__U22(mark(X1123), X2123, X382), X2, X3) [2]
   mark(U11(x(X1124, X2124), X2, X3)) -> a__U11(a__x(mark(X1124), mark(X2124)), X2, X3) [2]
   mark(U11(tt, X2, X3)) -> a__U11(tt, X2, X3) [2]
   mark(U11(s(X49), X2, X3)) -> a__U11(s(mark(X49)), X2, X3) [2]
   mark(U11(0, X2, X3)) -> a__U11(0, X2, X3) [2]
   mark(U12(U11(X1125, X2125, X383), X2, X3)) -> a__U12(a__U11(mark(X1125), X2125, X383), X2, X3) [2]
   mark(U12(U12(X1126, X2126, X384), X2, X3)) -> a__U12(a__U12(mark(X1126), X2126, X384), X2, X3) [2]
   mark(U12(plus(X1127, X2127), X2, X3)) -> a__U12(a__plus(mark(X1127), mark(X2127)), X2, X3) [2]
   mark(U12(U21(X1128, X2128, X385), X2, X3)) -> a__U12(a__U21(mark(X1128), X2128, X385), X2, X3) [2]
   mark(U12(U22(X1129, X2129, X386), X2, X3)) -> a__U12(a__U22(mark(X1129), X2129, X386), X2, X3) [2]
   mark(U12(x(X1130, X2130), X2, X3)) -> a__U12(a__x(mark(X1130), mark(X2130)), X2, X3) [2]
   mark(U12(tt, X2, X3)) -> a__U12(tt, X2, X3) [2]
   mark(U12(s(X50), X2, X3)) -> a__U12(s(mark(X50)), X2, X3) [2]
   mark(U12(0, X2, X3)) -> a__U12(0, X2, X3) [2]
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1]
   mark(U21(U11(X1191, X2191, X3127), X2, X3)) -> a__U21(a__U11(mark(X1191), X2191, X3127), X2, X3) [2]
   mark(U21(U12(X1192, X2192, X3128), X2, X3)) -> a__U21(a__U12(mark(X1192), X2192, X3128), X2, X3) [2]
   mark(U21(plus(X1193, X2193), X2, X3)) -> a__U21(a__plus(mark(X1193), mark(X2193)), X2, X3) [2]
   mark(U21(U21(X1194, X2194, X3129), X2, X3)) -> a__U21(a__U21(mark(X1194), X2194, X3129), X2, X3) [2]
   mark(U21(U22(X1195, X2195, X3130), X2, X3)) -> a__U21(a__U22(mark(X1195), X2195, X3130), X2, X3) [2]
   mark(U21(x(X1196, X2196), X2, X3)) -> a__U21(a__x(mark(X1196), mark(X2196)), X2, X3) [2]
   mark(U21(tt, X2, X3)) -> a__U21(tt, X2, X3) [2]
   mark(U21(s(X61), X2, X3)) -> a__U21(s(mark(X61)), X2, X3) [2]
   mark(U21(0, X2, X3)) -> a__U21(0, X2, X3) [2]
   mark(U22(U11(X1197, X2197, X3131), X2, X3)) -> a__U22(a__U11(mark(X1197), X2197, X3131), X2, X3) [2]
   mark(U22(U12(X1198, X2198, X3132), X2, X3)) -> a__U22(a__U12(mark(X1198), X2198, X3132), X2, X3) [2]
   mark(U22(plus(X1199, X2199), X2, X3)) -> a__U22(a__plus(mark(X1199), mark(X2199)), X2, X3) [2]
   mark(U22(U21(X1200, X2200, X3133), X2, X3)) -> a__U22(a__U21(mark(X1200), X2200, X3133), X2, X3) [2]
   mark(U22(U22(X1201, X2201, X3134), X2, X3)) -> a__U22(a__U22(mark(X1201), X2201, X3134), X2, X3) [2]
   mark(U22(x(X1202, X2202), X2, X3)) -> a__U22(a__x(mark(X1202), mark(X2202)), X2, X3) [2]
   mark(U22(tt, X2, X3)) -> a__U22(tt, X2, X3) [2]
   mark(U22(s(X62), X2, X3)) -> a__U22(s(mark(X62)), X2, X3) [2]
   mark(U22(0, X2, X3)) -> a__U22(0, X2, X3) [2]
   mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) [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, X3) -> U12(X1, X2, X3) [1]
   a__plus(X1, X2) -> plus(X1, X2) [1]
   a__U21(X1, X2, X3) -> U21(X1, X2, X3) [1]
   a__U22(X1, X2, X3) -> U22(X1, X2, X3) [1]
   a__x(X1, X2) -> x(X1, X2) [1]

The TRS has the following type information:
a__U11 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
tt :: tt:s:0:U11:U12:plus:U21:U22:x
a__U12 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
s :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
a__plus :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
mark :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
a__U21 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
a__U22 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
a__x :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
0 :: tt:s:0:U11:U12:plus:U21:U22:x
U11 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
U12 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
plus :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
U21 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
U22 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
x :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x

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

(277) 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

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

(278)
Obligation:
Complexity RNTS consisting of the following rules:

   a__U11(z, z', z'') -{ 1 }-> a__U12(1, M, N) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0
   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', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0
   a__U12(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__U21(z, z', z'') -{ 1 }-> a__U22(1, M, N) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0
   a__U21(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__U22(z, z', z'') -{ 1 }-> a__plus(a__x(mark(N), mark(M)), mark(N)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0
   a__U22(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__plus(z, z') -{ 1 }-> mark(N) :|: z = N, z' = 0, N >= 0
   a__plus(z, z') -{ 1 }-> a__U11(1, M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0
   a__plus(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__x(z, z') -{ 1 }-> a__U21(1, M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0
   a__x(z, z') -{ 1 }-> 0 :|: z = N, z' = 0, N >= 0
   a__x(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   mark(z) -{ 1 }-> a__x(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 2 }-> a__U22(a__x(mark(X1202), mark(X2202)), X2, X3) :|: z = 1 + (1 + X1202 + X2202) + X2 + X3, X2202 >= 0, X3 >= 0, X2 >= 0, X1202 >= 0
   mark(z) -{ 2 }-> a__U22(a__plus(mark(X1199), mark(X2199)), X2, X3) :|: z = 1 + (1 + X1199 + X2199) + X2 + X3, X2199 >= 0, X3 >= 0, X2 >= 0, X1199 >= 0
   mark(z) -{ 2 }-> a__U22(a__U22(mark(X1201), X2201, X3134), X2, X3) :|: X2201 >= 0, X3134 >= 0, z = 1 + (1 + X1201 + X2201 + X3134) + X2 + X3, X3 >= 0, X2 >= 0, X1201 >= 0
   mark(z) -{ 2 }-> a__U22(a__U21(mark(X1200), X2200, X3133), X2, X3) :|: z = 1 + (1 + X1200 + X2200 + X3133) + X2 + X3, X3133 >= 0, X2200 >= 0, X3 >= 0, X2 >= 0, X1200 >= 0
   mark(z) -{ 2 }-> a__U22(a__U12(mark(X1198), X2198, X3132), X2, X3) :|: X1198 >= 0, X3132 >= 0, X2198 >= 0, z = 1 + (1 + X1198 + X2198 + X3132) + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U22(a__U11(mark(X1197), X2197, X3131), X2, X3) :|: X2197 >= 0, z = 1 + (1 + X1197 + X2197 + X3131) + X2 + X3, X3 >= 0, X1197 >= 0, X2 >= 0, X3131 >= 0
   mark(z) -{ 2 }-> a__U22(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U22(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U22(1 + mark(X62), X2, X3) :|: z = 1 + (1 + X62) + X2 + X3, X3 >= 0, X62 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__x(mark(X1196), mark(X2196)), X2, X3) :|: X1196 >= 0, X3 >= 0, z = 1 + (1 + X1196 + X2196) + X2 + X3, X2 >= 0, X2196 >= 0
   mark(z) -{ 2 }-> a__U21(a__plus(mark(X1193), mark(X2193)), X2, X3) :|: X2193 >= 0, X3 >= 0, X1193 >= 0, z = 1 + (1 + X1193 + X2193) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__U22(mark(X1195), X2195, X3130), X2, X3) :|: X1195 >= 0, X3 >= 0, z = 1 + (1 + X1195 + X2195 + X3130) + X2 + X3, X2 >= 0, X2195 >= 0, X3130 >= 0
   mark(z) -{ 2 }-> a__U21(a__U21(mark(X1194), X2194, X3129), X2, X3) :|: X3129 >= 0, X1194 >= 0, X3 >= 0, z = 1 + (1 + X1194 + X2194 + X3129) + X2 + X3, X2 >= 0, X2194 >= 0
   mark(z) -{ 2 }-> a__U21(a__U12(mark(X1192), X2192, X3128), X2, X3) :|: X2192 >= 0, X3 >= 0, z = 1 + (1 + X1192 + X2192 + X3128) + X2 + X3, X2 >= 0, X1192 >= 0, X3128 >= 0
   mark(z) -{ 2 }-> a__U21(a__U11(mark(X1191), X2191, X3127), X2, X3) :|: X1191 >= 0, z = 1 + (1 + X1191 + X2191 + X3127) + X2 + X3, X2191 >= 0, X3 >= 0, X3127 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(1 + mark(X61), X2, X3) :|: z = 1 + (1 + X61) + X2 + X3, X61 >= 0, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U12(a__x(mark(X1130), mark(X2130)), X2, X3) :|: X2130 >= 0, X3 >= 0, z = 1 + (1 + X1130 + X2130) + X2 + X3, X1130 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U12(a__plus(mark(X1127), mark(X2127)), X2, X3) :|: X2127 >= 0, X3 >= 0, X1127 >= 0, z = 1 + (1 + X1127 + X2127) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U12(a__U22(mark(X1129), X2129, X386), X2, X3) :|: X1129 >= 0, z = 1 + (1 + X1129 + X2129 + X386) + X2 + X3, X2129 >= 0, X3 >= 0, X2 >= 0, X386 >= 0
   mark(z) -{ 2 }-> a__U12(a__U21(mark(X1128), X2128, X385), X2, X3) :|: X385 >= 0, X2128 >= 0, z = 1 + (1 + X1128 + X2128 + X385) + X2 + X3, X3 >= 0, X1128 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U12(a__U12(mark(X1126), X2126, X384), X2, X3) :|: z = 1 + (1 + X1126 + X2126 + X384) + X2 + X3, X384 >= 0, X1126 >= 0, X3 >= 0, X2 >= 0, X2126 >= 0
   mark(z) -{ 2 }-> a__U12(a__U11(mark(X1125), X2125, X383), X2, X3) :|: X1125 >= 0, X383 >= 0, X3 >= 0, z = 1 + (1 + X1125 + X2125 + X383) + X2 + X3, X2 >= 0, X2125 >= 0
   mark(z) -{ 2 }-> a__U12(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U12(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U12(1 + mark(X50), X2, X3) :|: X50 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X50) + X2 + X3
   mark(z) -{ 2 }-> a__U11(a__x(mark(X1124), mark(X2124)), X2, X3) :|: z = 1 + (1 + X1124 + X2124) + X2 + X3, X3 >= 0, X1124 >= 0, X2 >= 0, X2124 >= 0
   mark(z) -{ 2 }-> a__U11(a__plus(mark(X1121), mark(X2121)), X2, X3) :|: X1121 >= 0, X2121 >= 0, X3 >= 0, z = 1 + (1 + X1121 + X2121) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U22(mark(X1123), X2123, X382), X2, X3) :|: X2123 >= 0, X382 >= 0, X3 >= 0, X1123 >= 0, z = 1 + (1 + X1123 + X2123 + X382) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U21(mark(X1122), X2122, X381), X2, X3) :|: X381 >= 0, z = 1 + (1 + X1122 + X2122 + X381) + X2 + X3, X2122 >= 0, X3 >= 0, X2 >= 0, X1122 >= 0
   mark(z) -{ 2 }-> a__U11(a__U12(mark(X1120), X2120, X380), X2, X3) :|: z = 1 + (1 + X1120 + X2120 + X380) + X2 + X3, X2120 >= 0, X3 >= 0, X1120 >= 0, X380 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U11(mark(X1119), X2119, X379), X2, X3) :|: X1119 >= 0, z = 1 + (1 + X1119 + X2119 + X379) + X2 + X3, X379 >= 0, X2119 >= 0, X3 >= 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(X49), X2, X3) :|: X49 >= 0, X3 >= 0, z = 1 + (1 + X49) + 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


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

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

(280)
Obligation:
Complexity RNTS consisting of the following rules:

   a__U11(z, z', z'') -{ 1 }-> a__U12(1, z', z'') :|: z = 1, z' >= 0, z'' >= 0
   a__U11(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0
   a__U12(z, z', z'') -{ 1 }-> 1 + a__plus(mark(z''), mark(z')) :|: z = 1, z' >= 0, z'' >= 0
   a__U12(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0
   a__U21(z, z', z'') -{ 1 }-> a__U22(1, z', z'') :|: z = 1, z' >= 0, z'' >= 0
   a__U21(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0
   a__U22(z, z', z'') -{ 1 }-> a__plus(a__x(mark(z''), mark(z')), mark(z'')) :|: z = 1, z' >= 0, z'' >= 0
   a__U22(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0
   a__plus(z, z') -{ 1 }-> mark(z) :|: z' = 0, z >= 0
   a__plus(z, z') -{ 1 }-> a__U11(1, z' - 1, z) :|: z' - 1 >= 0, z >= 0
   a__plus(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   a__x(z, z') -{ 1 }-> a__U21(1, z' - 1, z) :|: z' - 1 >= 0, z >= 0
   a__x(z, z') -{ 1 }-> 0 :|: z' = 0, z >= 0
   a__x(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   mark(z) -{ 1 }-> a__x(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 2 }-> a__U22(a__x(mark(X1202), mark(X2202)), X2, X3) :|: z = 1 + (1 + X1202 + X2202) + X2 + X3, X2202 >= 0, X3 >= 0, X2 >= 0, X1202 >= 0
   mark(z) -{ 2 }-> a__U22(a__plus(mark(X1199), mark(X2199)), X2, X3) :|: z = 1 + (1 + X1199 + X2199) + X2 + X3, X2199 >= 0, X3 >= 0, X2 >= 0, X1199 >= 0
   mark(z) -{ 2 }-> a__U22(a__U22(mark(X1201), X2201, X3134), X2, X3) :|: X2201 >= 0, X3134 >= 0, z = 1 + (1 + X1201 + X2201 + X3134) + X2 + X3, X3 >= 0, X2 >= 0, X1201 >= 0
   mark(z) -{ 2 }-> a__U22(a__U21(mark(X1200), X2200, X3133), X2, X3) :|: z = 1 + (1 + X1200 + X2200 + X3133) + X2 + X3, X3133 >= 0, X2200 >= 0, X3 >= 0, X2 >= 0, X1200 >= 0
   mark(z) -{ 2 }-> a__U22(a__U12(mark(X1198), X2198, X3132), X2, X3) :|: X1198 >= 0, X3132 >= 0, X2198 >= 0, z = 1 + (1 + X1198 + X2198 + X3132) + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U22(a__U11(mark(X1197), X2197, X3131), X2, X3) :|: X2197 >= 0, z = 1 + (1 + X1197 + X2197 + X3131) + X2 + X3, X3 >= 0, X1197 >= 0, X2 >= 0, X3131 >= 0
   mark(z) -{ 2 }-> a__U22(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U22(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U22(1 + mark(X62), X2, X3) :|: z = 1 + (1 + X62) + X2 + X3, X3 >= 0, X62 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__x(mark(X1196), mark(X2196)), X2, X3) :|: X1196 >= 0, X3 >= 0, z = 1 + (1 + X1196 + X2196) + X2 + X3, X2 >= 0, X2196 >= 0
   mark(z) -{ 2 }-> a__U21(a__plus(mark(X1193), mark(X2193)), X2, X3) :|: X2193 >= 0, X3 >= 0, X1193 >= 0, z = 1 + (1 + X1193 + X2193) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__U22(mark(X1195), X2195, X3130), X2, X3) :|: X1195 >= 0, X3 >= 0, z = 1 + (1 + X1195 + X2195 + X3130) + X2 + X3, X2 >= 0, X2195 >= 0, X3130 >= 0
   mark(z) -{ 2 }-> a__U21(a__U21(mark(X1194), X2194, X3129), X2, X3) :|: X3129 >= 0, X1194 >= 0, X3 >= 0, z = 1 + (1 + X1194 + X2194 + X3129) + X2 + X3, X2 >= 0, X2194 >= 0
   mark(z) -{ 2 }-> a__U21(a__U12(mark(X1192), X2192, X3128), X2, X3) :|: X2192 >= 0, X3 >= 0, z = 1 + (1 + X1192 + X2192 + X3128) + X2 + X3, X2 >= 0, X1192 >= 0, X3128 >= 0
   mark(z) -{ 2 }-> a__U21(a__U11(mark(X1191), X2191, X3127), X2, X3) :|: X1191 >= 0, z = 1 + (1 + X1191 + X2191 + X3127) + X2 + X3, X2191 >= 0, X3 >= 0, X3127 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(1 + mark(X61), X2, X3) :|: z = 1 + (1 + X61) + X2 + X3, X61 >= 0, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U12(a__x(mark(X1130), mark(X2130)), X2, X3) :|: X2130 >= 0, X3 >= 0, z = 1 + (1 + X1130 + X2130) + X2 + X3, X1130 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U12(a__plus(mark(X1127), mark(X2127)), X2, X3) :|: X2127 >= 0, X3 >= 0, X1127 >= 0, z = 1 + (1 + X1127 + X2127) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U12(a__U22(mark(X1129), X2129, X386), X2, X3) :|: X1129 >= 0, z = 1 + (1 + X1129 + X2129 + X386) + X2 + X3, X2129 >= 0, X3 >= 0, X2 >= 0, X386 >= 0
   mark(z) -{ 2 }-> a__U12(a__U21(mark(X1128), X2128, X385), X2, X3) :|: X385 >= 0, X2128 >= 0, z = 1 + (1 + X1128 + X2128 + X385) + X2 + X3, X3 >= 0, X1128 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U12(a__U12(mark(X1126), X2126, X384), X2, X3) :|: z = 1 + (1 + X1126 + X2126 + X384) + X2 + X3, X384 >= 0, X1126 >= 0, X3 >= 0, X2 >= 0, X2126 >= 0
   mark(z) -{ 2 }-> a__U12(a__U11(mark(X1125), X2125, X383), X2, X3) :|: X1125 >= 0, X383 >= 0, X3 >= 0, z = 1 + (1 + X1125 + X2125 + X383) + X2 + X3, X2 >= 0, X2125 >= 0
   mark(z) -{ 2 }-> a__U12(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U12(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U12(1 + mark(X50), X2, X3) :|: X50 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X50) + X2 + X3
   mark(z) -{ 2 }-> a__U11(a__x(mark(X1124), mark(X2124)), X2, X3) :|: z = 1 + (1 + X1124 + X2124) + X2 + X3, X3 >= 0, X1124 >= 0, X2 >= 0, X2124 >= 0
   mark(z) -{ 2 }-> a__U11(a__plus(mark(X1121), mark(X2121)), X2, X3) :|: X1121 >= 0, X2121 >= 0, X3 >= 0, z = 1 + (1 + X1121 + X2121) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U22(mark(X1123), X2123, X382), X2, X3) :|: X2123 >= 0, X382 >= 0, X3 >= 0, X1123 >= 0, z = 1 + (1 + X1123 + X2123 + X382) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U21(mark(X1122), X2122, X381), X2, X3) :|: X381 >= 0, z = 1 + (1 + X1122 + X2122 + X381) + X2 + X3, X2122 >= 0, X3 >= 0, X2 >= 0, X1122 >= 0
   mark(z) -{ 2 }-> a__U11(a__U12(mark(X1120), X2120, X380), X2, X3) :|: z = 1 + (1 + X1120 + X2120 + X380) + X2 + X3, X2120 >= 0, X3 >= 0, X1120 >= 0, X380 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U11(mark(X1119), X2119, X379), X2, X3) :|: X1119 >= 0, z = 1 + (1 + X1119 + X2119 + X379) + X2 + X3, X379 >= 0, X2119 >= 0, X3 >= 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(X49), X2, X3) :|: X49 >= 0, X3 >= 0, z = 1 + (1 + X49) + X2 + X3, X2 >= 0
   mark(z) -{ 1 }-> 1 :|: z = 1
   mark(z) -{ 1 }-> 0 :|: z = 0
   mark(z) -{ 1 }-> 1 + mark(z - 1) :|: z - 1 >= 0


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

(281) 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

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

(282)
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, M, N) -> a__U12(tt, M, N) [1]
   a__U12(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1]
   a__U21(tt, M, N) -> a__U22(tt, M, N) [1]
   a__U22(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)) [1]
   a__plus(N, 0) -> mark(N) [1]
   a__plus(N, s(M)) -> a__U11(tt, M, N) [1]
   a__x(N, 0) -> 0 [1]
   a__x(N, s(M)) -> a__U21(tt, M, N) [1]
   mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) [1]
   mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) [1]
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1]
   mark(U21(X1, X2, X3)) -> a__U21(mark(X1), X2, X3) [1]
   mark(U22(X1, X2, X3)) -> a__U22(mark(X1), X2, X3) [1]
   mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) [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, X3) -> U12(X1, X2, X3) [1]
   a__plus(X1, X2) -> plus(X1, X2) [1]
   a__U21(X1, X2, X3) -> U21(X1, X2, X3) [1]
   a__U22(X1, X2, X3) -> U22(X1, X2, X3) [1]
   a__x(X1, X2) -> x(X1, X2) [1]

The TRS has the following type information:
a__U11 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
tt :: tt:s:0:U11:U12:plus:U21:U22:x
a__U12 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
s :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
a__plus :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
mark :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
a__U21 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
a__U22 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
a__x :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
0 :: tt:s:0:U11:U12:plus:U21:U22:x
U11 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
U12 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
plus :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
U21 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
U22 :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x
x :: tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x -> tt:s:0:U11:U12:plus:U21:U22:x

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

(283) 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

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

(284)
Obligation:
Complexity RNTS consisting of the following rules:

   a__U11(z, z', z'') -{ 1 }-> a__U12(1, M, N) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0
   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', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0
   a__U12(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__U21(z, z', z'') -{ 1 }-> a__U22(1, M, N) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0
   a__U21(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__U22(z, z', z'') -{ 1 }-> a__plus(a__x(mark(N), mark(M)), mark(N)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0
   a__U22(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__plus(z, z') -{ 1 }-> mark(N) :|: z = N, z' = 0, N >= 0
   a__plus(z, z') -{ 1 }-> a__U11(1, M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0
   a__plus(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__x(z, z') -{ 1 }-> a__U21(1, M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0
   a__x(z, z') -{ 1 }-> 0 :|: z = N, z' = 0, N >= 0
   a__x(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   mark(z) -{ 1 }-> a__x(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U22(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0
   mark(z) -{ 1 }-> a__U21(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0
   mark(z) -{ 1 }-> a__U12(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0
   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.