KILLED proof of input_p6mpofGBvT.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (14) CpxRNTS (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRNTS (17) CompletionProof [UPPER BOUND(ID), 0 ms] (18) CpxTypedWeightedCompleteTrs (19) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (20) CpxRNTS (21) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (22) CdtProblem (23) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (24) CdtProblem (25) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (26) CdtProblem (27) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (28) CdtProblem (29) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CdtProblem (31) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (32) CdtProblem (33) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (34) CdtProblem (35) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CdtProblem (37) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CdtProblem (39) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CdtProblem (43) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CdtProblem (47) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 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) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 18 ms] (106) CdtProblem (107) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5269 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5646 ms] (118) CdtProblem (119) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 7 ms] (120) CdtProblem (121) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 178 ms] (122) CdtProblem (123) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 550 ms] (124) CdtProblem (125) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 2852 ms] (126) CdtProblem ---------------------------------------- (0) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__2nd(cons1(X, cons(Y, Z))) -> mark(Y) a__2nd(cons(X, X1)) -> a__2nd(cons1(mark(X), mark(X1))) a__from(X) -> cons(mark(X), from(s(X))) mark(2nd(X)) -> a__2nd(mark(X)) mark(from(X)) -> a__from(mark(X)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(s(X)) -> s(mark(X)) mark(cons1(X1, X2)) -> cons1(mark(X1), mark(X2)) a__2nd(X) -> 2nd(X) a__from(X) -> from(X) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__2nd(cons1(X, cons(Y, Z))) -> mark(Y) a__2nd(cons(X, X1)) -> a__2nd(cons1(mark(X), mark(X1))) a__from(X) -> cons(mark(X), from(s(X))) mark(2nd(X)) -> a__2nd(mark(X)) mark(from(X)) -> a__from(mark(X)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(s(X)) -> s(mark(X)) mark(cons1(X1, X2)) -> cons1(mark(X1), mark(X2)) a__2nd(X) -> 2nd(X) a__from(X) -> from(X) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (3) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (4) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__2nd(cons1(X, cons(Y, Z))) -> mark(Y) a__2nd(cons(X, X1)) -> a__2nd(cons1(mark(X), mark(X1))) a__from(X) -> cons(mark(X), from(s(X))) mark(2nd(X)) -> a__2nd(mark(X)) mark(from(X)) -> a__from(mark(X)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(s(X)) -> s(mark(X)) mark(cons1(X1, X2)) -> cons1(mark(X1), mark(X2)) a__2nd(X) -> 2nd(X) a__from(X) -> from(X) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (5) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__2nd(cons1(X, cons(Y, Z))) -> mark(Y) [1] a__2nd(cons(X, X1)) -> a__2nd(cons1(mark(X), mark(X1))) [1] a__from(X) -> cons(mark(X), from(s(X))) [1] mark(2nd(X)) -> a__2nd(mark(X)) [1] mark(from(X)) -> a__from(mark(X)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(s(X)) -> s(mark(X)) [1] mark(cons1(X1, X2)) -> cons1(mark(X1), mark(X2)) [1] a__2nd(X) -> 2nd(X) [1] a__from(X) -> from(X) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__2nd(cons1(X, cons(Y, Z))) -> mark(Y) [1] a__2nd(cons(X, X1)) -> a__2nd(cons1(mark(X), mark(X1))) [1] a__from(X) -> cons(mark(X), from(s(X))) [1] mark(2nd(X)) -> a__2nd(mark(X)) [1] mark(from(X)) -> a__from(mark(X)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(s(X)) -> s(mark(X)) [1] mark(cons1(X1, X2)) -> cons1(mark(X1), mark(X2)) [1] a__2nd(X) -> 2nd(X) [1] a__from(X) -> from(X) [1] The TRS has the following type information: a__2nd :: cons:cons1:s:from:2nd -> cons:cons1:s:from:2nd cons1 :: cons:cons1:s:from:2nd -> cons:cons1:s:from:2nd -> cons:cons1:s:from:2nd cons :: cons:cons1:s:from:2nd -> cons:cons1:s:from:2nd -> cons:cons1:s:from:2nd mark :: cons:cons1:s:from:2nd -> cons:cons1:s:from:2nd a__from :: cons:cons1:s:from:2nd -> cons:cons1:s:from:2nd from :: cons:cons1:s:from:2nd -> cons:cons1:s:from:2nd s :: cons:cons1:s:from:2nd -> cons:cons1:s:from:2nd 2nd :: cons:cons1:s:from:2nd -> cons:cons1:s:from:2nd Rewrite Strategy: INNERMOST ---------------------------------------- (9) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: none (c) The following functions are completely defined: mark_1 a__2nd_1 a__from_1 Due to the following rules being added: mark(v0) -> const [0] And the following fresh constants: const ---------------------------------------- (10) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__2nd(cons1(X, cons(Y, Z))) -> mark(Y) [1] a__2nd(cons(X, X1)) -> a__2nd(cons1(mark(X), mark(X1))) [1] a__from(X) -> cons(mark(X), from(s(X))) [1] mark(2nd(X)) -> a__2nd(mark(X)) [1] mark(from(X)) -> a__from(mark(X)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(s(X)) -> s(mark(X)) [1] mark(cons1(X1, X2)) -> cons1(mark(X1), mark(X2)) [1] a__2nd(X) -> 2nd(X) [1] a__from(X) -> from(X) [1] mark(v0) -> const [0] The TRS has the following type information: a__2nd :: cons:cons1:s:from:2nd:const -> cons:cons1:s:from:2nd:const cons1 :: cons:cons1:s:from:2nd:const -> cons:cons1:s:from:2nd:const -> cons:cons1:s:from:2nd:const cons :: cons:cons1:s:from:2nd:const -> cons:cons1:s:from:2nd:const -> cons:cons1:s:from:2nd:const mark :: cons:cons1:s:from:2nd:const -> cons:cons1:s:from:2nd:const a__from :: cons:cons1:s:from:2nd:const -> cons:cons1:s:from:2nd:const from :: cons:cons1:s:from:2nd:const -> cons:cons1:s:from:2nd:const s :: cons:cons1:s:from:2nd:const -> cons:cons1:s:from:2nd:const 2nd :: cons:cons1:s:from:2nd:const -> cons:cons1:s:from:2nd:const const :: cons:cons1:s:from:2nd:const Rewrite Strategy: INNERMOST ---------------------------------------- (11) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (12) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__2nd(cons1(X, cons(Y, Z))) -> mark(Y) [1] a__2nd(cons(X, X1)) -> a__2nd(cons1(mark(X), mark(X1))) [1] a__from(X) -> cons(mark(X), from(s(X))) [1] mark(2nd(2nd(X36))) -> a__2nd(a__2nd(mark(X36))) [2] mark(2nd(from(X37))) -> a__2nd(a__from(mark(X37))) [2] mark(2nd(cons(X116, X214))) -> a__2nd(cons(mark(X116), X214)) [2] mark(2nd(s(X38))) -> a__2nd(s(mark(X38))) [2] mark(2nd(cons1(X117, X215))) -> a__2nd(cons1(mark(X117), mark(X215))) [2] mark(2nd(X)) -> a__2nd(const) [1] mark(from(2nd(X39))) -> a__from(a__2nd(mark(X39))) [2] mark(from(from(X40))) -> a__from(a__from(mark(X40))) [2] mark(from(cons(X118, X216))) -> a__from(cons(mark(X118), X216)) [2] mark(from(s(X41))) -> a__from(s(mark(X41))) [2] mark(from(cons1(X119, X217))) -> a__from(cons1(mark(X119), mark(X217))) [2] mark(from(X)) -> a__from(const) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(s(X)) -> s(mark(X)) [1] mark(cons1(X1, X2)) -> cons1(mark(X1), mark(X2)) [1] a__2nd(X) -> 2nd(X) [1] a__from(X) -> from(X) [1] mark(v0) -> const [0] The TRS has the following type information: a__2nd :: cons:cons1:s:from:2nd:const -> cons:cons1:s:from:2nd:const cons1 :: cons:cons1:s:from:2nd:const -> cons:cons1:s:from:2nd:const -> cons:cons1:s:from:2nd:const cons :: cons:cons1:s:from:2nd:const -> cons:cons1:s:from:2nd:const -> cons:cons1:s:from:2nd:const mark :: cons:cons1:s:from:2nd:const -> cons:cons1:s:from:2nd:const a__from :: cons:cons1:s:from:2nd:const -> cons:cons1:s:from:2nd:const from :: cons:cons1:s:from:2nd:const -> cons:cons1:s:from:2nd:const s :: cons:cons1:s:from:2nd:const -> cons:cons1:s:from:2nd:const 2nd :: cons:cons1:s:from:2nd:const -> cons:cons1:s:from:2nd:const const :: cons:cons1:s:from:2nd:const Rewrite Strategy: INNERMOST ---------------------------------------- (13) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: const => 0 ---------------------------------------- (14) Obligation: Complexity RNTS consisting of the following rules: a__2nd(z) -{ 1 }-> mark(Y) :|: z = 1 + X + (1 + Y + Z), Z >= 0, Y >= 0, X >= 0 a__2nd(z) -{ 1 }-> a__2nd(1 + mark(X) + mark(X1)) :|: X1 >= 0, X >= 0, z = 1 + X + X1 a__2nd(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__from(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__from(z) -{ 1 }-> 1 + mark(X) + (1 + (1 + X)) :|: X >= 0, z = X mark(z) -{ 2 }-> a__from(a__from(mark(X40))) :|: z = 1 + (1 + X40), X40 >= 0 mark(z) -{ 2 }-> a__from(a__2nd(mark(X39))) :|: z = 1 + (1 + X39), X39 >= 0 mark(z) -{ 1 }-> a__from(0) :|: z = 1 + X, X >= 0 mark(z) -{ 2 }-> a__from(1 + mark(X41)) :|: X41 >= 0, z = 1 + (1 + X41) mark(z) -{ 2 }-> a__from(1 + mark(X118) + X216) :|: X118 >= 0, X216 >= 0, z = 1 + (1 + X118 + X216) mark(z) -{ 2 }-> a__from(1 + mark(X119) + mark(X217)) :|: z = 1 + (1 + X119 + X217), X119 >= 0, X217 >= 0 mark(z) -{ 2 }-> a__2nd(a__from(mark(X37))) :|: X37 >= 0, z = 1 + (1 + X37) mark(z) -{ 2 }-> a__2nd(a__2nd(mark(X36))) :|: X36 >= 0, z = 1 + (1 + X36) mark(z) -{ 1 }-> a__2nd(0) :|: z = 1 + X, X >= 0 mark(z) -{ 2 }-> a__2nd(1 + mark(X38)) :|: X38 >= 0, z = 1 + (1 + X38) mark(z) -{ 2 }-> a__2nd(1 + mark(X116) + X214) :|: X214 >= 0, z = 1 + (1 + X116 + X214), X116 >= 0 mark(z) -{ 2 }-> a__2nd(1 + mark(X117) + mark(X215)) :|: z = 1 + (1 + X117 + X215), X117 >= 0, X215 >= 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> 1 + mark(X1) + mark(X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 ---------------------------------------- (15) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (16) Obligation: Complexity RNTS consisting of the following rules: a__2nd(z) -{ 1 }-> mark(Y) :|: z = 1 + X + (1 + Y + Z), Z >= 0, Y >= 0, X >= 0 a__2nd(z) -{ 1 }-> a__2nd(1 + mark(X) + mark(X1)) :|: X1 >= 0, X >= 0, z = 1 + X + X1 a__2nd(z) -{ 1 }-> 1 + z :|: z >= 0 a__from(z) -{ 1 }-> 1 + z :|: z >= 0 a__from(z) -{ 1 }-> 1 + mark(z) + (1 + (1 + z)) :|: z >= 0 mark(z) -{ 2 }-> a__from(a__from(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__from(a__2nd(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 1 }-> a__from(0) :|: z - 1 >= 0 mark(z) -{ 2 }-> a__from(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__from(1 + mark(X118) + X216) :|: X118 >= 0, X216 >= 0, z = 1 + (1 + X118 + X216) mark(z) -{ 2 }-> a__from(1 + mark(X119) + mark(X217)) :|: z = 1 + (1 + X119 + X217), X119 >= 0, X217 >= 0 mark(z) -{ 2 }-> a__2nd(a__from(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__2nd(a__2nd(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 1 }-> a__2nd(0) :|: z - 1 >= 0 mark(z) -{ 2 }-> a__2nd(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__2nd(1 + mark(X116) + X214) :|: X214 >= 0, z = 1 + (1 + X116 + X214), X116 >= 0 mark(z) -{ 2 }-> a__2nd(1 + mark(X117) + mark(X215)) :|: z = 1 + (1 + X117 + X215), X117 >= 0, X215 >= 0 mark(z) -{ 0 }-> 0 :|: z >= 0 mark(z) -{ 1 }-> 1 + mark(z - 1) :|: z - 1 >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> 1 + mark(X1) + mark(X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 ---------------------------------------- (17) 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: mark(v0) -> null_mark [0] And the following fresh constants: null_mark ---------------------------------------- (18) 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__2nd(cons1(X, cons(Y, Z))) -> mark(Y) [1] a__2nd(cons(X, X1)) -> a__2nd(cons1(mark(X), mark(X1))) [1] a__from(X) -> cons(mark(X), from(s(X))) [1] mark(2nd(X)) -> a__2nd(mark(X)) [1] mark(from(X)) -> a__from(mark(X)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(s(X)) -> s(mark(X)) [1] mark(cons1(X1, X2)) -> cons1(mark(X1), mark(X2)) [1] a__2nd(X) -> 2nd(X) [1] a__from(X) -> from(X) [1] mark(v0) -> null_mark [0] The TRS has the following type information: a__2nd :: cons:cons1:s:from:2nd:null_mark -> cons:cons1:s:from:2nd:null_mark cons1 :: cons:cons1:s:from:2nd:null_mark -> cons:cons1:s:from:2nd:null_mark -> cons:cons1:s:from:2nd:null_mark cons :: cons:cons1:s:from:2nd:null_mark -> cons:cons1:s:from:2nd:null_mark -> cons:cons1:s:from:2nd:null_mark mark :: cons:cons1:s:from:2nd:null_mark -> cons:cons1:s:from:2nd:null_mark a__from :: cons:cons1:s:from:2nd:null_mark -> cons:cons1:s:from:2nd:null_mark from :: cons:cons1:s:from:2nd:null_mark -> cons:cons1:s:from:2nd:null_mark s :: cons:cons1:s:from:2nd:null_mark -> cons:cons1:s:from:2nd:null_mark 2nd :: cons:cons1:s:from:2nd:null_mark -> cons:cons1:s:from:2nd:null_mark null_mark :: cons:cons1:s:from:2nd:null_mark Rewrite Strategy: INNERMOST ---------------------------------------- (19) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: null_mark => 0 ---------------------------------------- (20) Obligation: Complexity RNTS consisting of the following rules: a__2nd(z) -{ 1 }-> mark(Y) :|: z = 1 + X + (1 + Y + Z), Z >= 0, Y >= 0, X >= 0 a__2nd(z) -{ 1 }-> a__2nd(1 + mark(X) + mark(X1)) :|: X1 >= 0, X >= 0, z = 1 + X + X1 a__2nd(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__from(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__from(z) -{ 1 }-> 1 + mark(X) + (1 + (1 + X)) :|: X >= 0, z = X mark(z) -{ 1 }-> a__from(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__2nd(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> 1 + mark(X1) + mark(X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (21) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (22) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__2ND(cons(z0, z1)) -> c1(A__2ND(cons1(mark(z0), mark(z1))), MARK(z0)) A__2ND(cons(z0, z1)) -> c2(A__2ND(cons1(mark(z0), mark(z1))), MARK(z1)) A__2ND(z0) -> c3 A__FROM(z0) -> c4(MARK(z0)) A__FROM(z0) -> c5 MARK(2nd(z0)) -> c6(A__2ND(mark(z0)), MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__2ND(cons(z0, z1)) -> c1(A__2ND(cons1(mark(z0), mark(z1))), MARK(z0)) A__2ND(cons(z0, z1)) -> c2(A__2ND(cons1(mark(z0), mark(z1))), MARK(z1)) A__2ND(z0) -> c3 A__FROM(z0) -> c4(MARK(z0)) A__FROM(z0) -> c5 MARK(2nd(z0)) -> c6(A__2ND(mark(z0)), MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c1_2, c2_2, c3, c4_1, c5, c6_2, c7_2, c8_1, c9_1, c10_1, c11_1 ---------------------------------------- (23) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__2ND(z0) -> c3 A__FROM(z0) -> c5 ---------------------------------------- (24) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__2ND(cons(z0, z1)) -> c1(A__2ND(cons1(mark(z0), mark(z1))), MARK(z0)) A__2ND(cons(z0, z1)) -> c2(A__2ND(cons1(mark(z0), mark(z1))), MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(2nd(z0)) -> c6(A__2ND(mark(z0)), MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__2ND(cons(z0, z1)) -> c1(A__2ND(cons1(mark(z0), mark(z1))), MARK(z0)) A__2ND(cons(z0, z1)) -> c2(A__2ND(cons1(mark(z0), mark(z1))), MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(2nd(z0)) -> c6(A__2ND(mark(z0)), MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c1_2, c2_2, c4_1, c6_2, c7_2, c8_1, c9_1, c10_1, c11_1 ---------------------------------------- (25) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__2ND(cons(z0, z1)) -> c1(A__2ND(cons1(mark(z0), mark(z1))), MARK(z0)) by A__2ND(cons(x0, 2nd(z0))) -> c1(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(x0)) A__2ND(cons(x0, from(z0))) -> c1(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(A__2ND(cons1(mark(x0), s(mark(z0)))), MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons1(mark(z0), mark(z1)))), MARK(x0)) A__2ND(cons(2nd(z0), x1)) -> c1(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(2nd(z0))) A__2ND(cons(from(z0), x1)) -> c1(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) ---------------------------------------- (26) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__2ND(cons(z0, z1)) -> c2(A__2ND(cons1(mark(z0), mark(z1))), MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(2nd(z0)) -> c6(A__2ND(mark(z0)), MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, 2nd(z0))) -> c1(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(x0)) A__2ND(cons(x0, from(z0))) -> c1(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(A__2ND(cons1(mark(x0), s(mark(z0)))), MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons1(mark(z0), mark(z1)))), MARK(x0)) A__2ND(cons(2nd(z0), x1)) -> c1(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(2nd(z0))) A__2ND(cons(from(z0), x1)) -> c1(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__2ND(cons(z0, z1)) -> c2(A__2ND(cons1(mark(z0), mark(z1))), MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(2nd(z0)) -> c6(A__2ND(mark(z0)), MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, 2nd(z0))) -> c1(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(x0)) A__2ND(cons(x0, from(z0))) -> c1(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(A__2ND(cons1(mark(x0), s(mark(z0)))), MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons1(mark(z0), mark(z1)))), MARK(x0)) A__2ND(cons(2nd(z0), x1)) -> c1(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(2nd(z0))) A__2ND(cons(from(z0), x1)) -> c1(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c2_2, c4_1, c6_2, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2 ---------------------------------------- (27) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (28) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__2ND(cons(z0, z1)) -> c2(A__2ND(cons1(mark(z0), mark(z1))), MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(2nd(z0)) -> c6(A__2ND(mark(z0)), MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, 2nd(z0))) -> c1(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(x0)) A__2ND(cons(x0, from(z0))) -> c1(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(2nd(z0), x1)) -> c1(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(2nd(z0))) A__2ND(cons(from(z0), x1)) -> c1(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__2ND(cons(z0, z1)) -> c2(A__2ND(cons1(mark(z0), mark(z1))), MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(2nd(z0)) -> c6(A__2ND(mark(z0)), MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, 2nd(z0))) -> c1(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(x0)) A__2ND(cons(x0, from(z0))) -> c1(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(2nd(z0), x1)) -> c1(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(2nd(z0))) A__2ND(cons(from(z0), x1)) -> c1(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c2_2, c4_1, c6_2, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1 ---------------------------------------- (29) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__2ND(cons(z0, z1)) -> c2(A__2ND(cons1(mark(z0), mark(z1))), MARK(z1)) by A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(x0, s(z0))) -> c2(A__2ND(cons1(mark(x0), s(mark(z0)))), MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons1(mark(z0), mark(z1)))), MARK(cons1(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) ---------------------------------------- (30) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(2nd(z0)) -> c6(A__2ND(mark(z0)), MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, 2nd(z0))) -> c1(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(x0)) A__2ND(cons(x0, from(z0))) -> c1(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(2nd(z0), x1)) -> c1(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(2nd(z0))) A__2ND(cons(from(z0), x1)) -> c1(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(x0, s(z0))) -> c2(A__2ND(cons1(mark(x0), s(mark(z0)))), MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons1(mark(z0), mark(z1)))), MARK(cons1(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(2nd(z0)) -> c6(A__2ND(mark(z0)), MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, 2nd(z0))) -> c1(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(x0)) A__2ND(cons(x0, from(z0))) -> c1(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(2nd(z0), x1)) -> c1(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(2nd(z0))) A__2ND(cons(from(z0), x1)) -> c1(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(x0, s(z0))) -> c2(A__2ND(cons1(mark(x0), s(mark(z0)))), MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons1(mark(z0), mark(z1)))), MARK(cons1(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c6_2, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2 ---------------------------------------- (31) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (32) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(2nd(z0)) -> c6(A__2ND(mark(z0)), MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, 2nd(z0))) -> c1(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(x0)) A__2ND(cons(x0, from(z0))) -> c1(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(2nd(z0), x1)) -> c1(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(2nd(z0))) A__2ND(cons(from(z0), x1)) -> c1(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(2nd(z0)) -> c6(A__2ND(mark(z0)), MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, 2nd(z0))) -> c1(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(x0)) A__2ND(cons(x0, from(z0))) -> c1(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(2nd(z0), x1)) -> c1(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(2nd(z0))) A__2ND(cons(from(z0), x1)) -> c1(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c6_2, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1 ---------------------------------------- (33) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(2nd(z0)) -> c6(A__2ND(mark(z0)), MARK(z0)) by MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(A__2ND(s(mark(z0))), MARK(s(z0))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) ---------------------------------------- (34) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, 2nd(z0))) -> c1(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(x0)) A__2ND(cons(x0, from(z0))) -> c1(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(2nd(z0), x1)) -> c1(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(2nd(z0))) A__2ND(cons(from(z0), x1)) -> c1(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(A__2ND(s(mark(z0))), MARK(s(z0))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, 2nd(z0))) -> c1(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(x0)) A__2ND(cons(x0, from(z0))) -> c1(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(2nd(z0), x1)) -> c1(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(2nd(z0))) A__2ND(cons(from(z0), x1)) -> c1(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(A__2ND(s(mark(z0))), MARK(s(z0))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2 ---------------------------------------- (35) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (36) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, 2nd(z0))) -> c1(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(x0)) A__2ND(cons(x0, from(z0))) -> c1(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(2nd(z0), x1)) -> c1(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(2nd(z0))) A__2ND(cons(from(z0), x1)) -> c1(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, 2nd(z0))) -> c1(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(x0)) A__2ND(cons(x0, from(z0))) -> c1(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(2nd(z0), x1)) -> c1(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(2nd(z0))) A__2ND(cons(from(z0), x1)) -> c1(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (37) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__2ND(cons(x0, 2nd(z0))) -> c1(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(x0)) by A__2ND(cons(x0, 2nd(x1))) -> c1(A__2ND(cons1(mark(x0), 2nd(mark(x1)))), MARK(x0)) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, from(z0))) -> c1(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(2nd(z0), x1)) -> c1(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(2nd(z0))) A__2ND(cons(from(z0), x1)) -> c1(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(x1))) -> c1(A__2ND(cons1(mark(x0), 2nd(mark(x1)))), MARK(x0)) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, from(z0))) -> c1(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(2nd(z0), x1)) -> c1(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(2nd(z0))) A__2ND(cons(from(z0), x1)) -> c1(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(x1))) -> c1(A__2ND(cons1(mark(x0), 2nd(mark(x1)))), MARK(x0)) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (39) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, from(z0))) -> c1(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(2nd(z0), x1)) -> c1(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(2nd(z0))) A__2ND(cons(from(z0), x1)) -> c1(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, from(z0))) -> c1(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(2nd(z0), x1)) -> c1(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(2nd(z0))) A__2ND(cons(from(z0), x1)) -> c1(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (41) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__2ND(cons(x0, from(z0))) -> c1(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(x0)) by A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), from(mark(x1)))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(2nd(z0), x1)) -> c1(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(2nd(z0))) A__2ND(cons(from(z0), x1)) -> c1(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), from(mark(x1)))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(2nd(z0), x1)) -> c1(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(2nd(z0))) A__2ND(cons(from(z0), x1)) -> c1(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), from(mark(x1)))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (43) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(2nd(z0), x1)) -> c1(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(2nd(z0))) A__2ND(cons(from(z0), x1)) -> c1(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(2nd(z0), x1)) -> c1(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(2nd(z0))) A__2ND(cons(from(z0), x1)) -> c1(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (45) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__2ND(cons(2nd(z0), x1)) -> c1(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(2nd(z0))) by A__2ND(cons(2nd(x0), 2nd(z0))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), a__2nd(mark(z0)))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), from(z0))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), a__from(mark(z0)))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), s(z0))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), s(mark(z0)))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons1(mark(z0), mark(z1)))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(from(z0), x1)) -> c1(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), s(z0))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), s(mark(z0)))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons1(mark(z0), mark(z1)))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(from(z0), x1)) -> c1(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), s(z0))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), s(mark(z0)))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons1(mark(z0), mark(z1)))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(from(z0), x1)) -> c1(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(from(z0), x1)) -> c1(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (49) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__2ND(cons(from(z0), x1)) -> c1(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(from(z0))) by A__2ND(cons(from(x0), 2nd(z0))) -> c1(A__2ND(cons1(a__from(mark(x0)), a__2nd(mark(z0)))), MARK(from(x0))) A__2ND(cons(from(x0), from(z0))) -> c1(A__2ND(cons1(a__from(mark(x0)), a__from(mark(z0)))), MARK(from(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(A__2ND(cons1(a__from(mark(x0)), s(mark(z0)))), MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons1(mark(z0), mark(z1)))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(A__2ND(cons1(a__from(mark(x0)), s(mark(z0)))), MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons1(mark(z0), mark(z1)))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(A__2ND(cons1(a__from(mark(x0)), s(mark(z0)))), MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons1(mark(z0), mark(z1)))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (51) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (53) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__2ND(cons(cons(z0, z1), x1)) -> c1(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons(z0, z1))) by A__2ND(cons(cons(x0, x1), 2nd(z0))) -> c1(A__2ND(cons1(cons(mark(x0), x1), a__2nd(mark(z0)))), MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), from(z0))) -> c1(A__2ND(cons1(cons(mark(x0), x1), a__from(mark(z0)))), MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(A__2ND(cons1(cons(mark(x0), x1), s(mark(z0)))), MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons1(mark(z0), mark(z1)))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(A__2ND(cons1(cons(mark(x0), x1), s(mark(z0)))), MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons1(mark(z0), mark(z1)))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(A__2ND(cons1(cons(mark(x0), x1), s(mark(z0)))), MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons1(mark(z0), mark(z1)))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (55) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (57) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__2ND(cons(s(z0), x1)) -> c1(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(s(z0))) by A__2ND(cons(s(x0), 2nd(z0))) -> c1(A__2ND(cons1(s(mark(x0)), a__2nd(mark(z0)))), MARK(s(x0))) A__2ND(cons(s(x0), from(z0))) -> c1(A__2ND(cons1(s(mark(x0)), a__from(mark(z0)))), MARK(s(x0))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(A__2ND(cons1(s(mark(x0)), s(mark(z0)))), MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons1(mark(z0), mark(z1)))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(A__2ND(cons1(s(mark(x0)), s(mark(z0)))), MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons1(mark(z0), mark(z1)))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(A__2ND(cons1(s(mark(x0)), s(mark(z0)))), MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons1(mark(z0), mark(z1)))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (59) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (61) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__2ND(cons(cons1(z0, z1), x1)) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(z0, z1))) by A__2ND(cons(cons1(x0, x1), 2nd(z0))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), a__2nd(mark(z0)))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), from(z0))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), a__from(mark(z0)))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), s(mark(z0)))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons1(mark(z0), mark(z1)))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), s(mark(z0)))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons1(mark(z0), mark(z1)))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), s(mark(z0)))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons1(mark(z0), mark(z1)))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (63) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (65) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__2ND(cons(x0, 2nd(z0))) -> c2(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(2nd(z0))) by A__2ND(cons(x0, 2nd(x1))) -> c2(A__2ND(cons1(mark(x0), 2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(A__2ND(cons1(mark(x0), 2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(A__2ND(cons1(mark(x0), 2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (69) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__2ND(cons(x0, from(z0))) -> c2(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(from(z0))) by A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (71) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (73) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__2ND(cons(2nd(z0), x1)) -> c2(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(x1)) by A__2ND(cons(2nd(x0), 2nd(z0))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(2nd(x0), from(z0))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), s(z0))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), s(mark(z0)))), MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons1(mark(z0), mark(z1)))), MARK(cons1(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), s(z0))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), s(mark(z0)))), MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons1(mark(z0), mark(z1)))), MARK(cons1(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), s(z0))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), s(mark(z0)))), MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons1(mark(z0), mark(z1)))), MARK(cons1(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (75) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (77) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__2ND(cons(from(z0), x1)) -> c2(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(x1)) by A__2ND(cons(from(x0), 2nd(z0))) -> c2(A__2ND(cons1(a__from(mark(x0)), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(from(x0), from(z0))) -> c2(A__2ND(cons1(a__from(mark(x0)), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), s(z0))) -> c2(A__2ND(cons1(a__from(mark(x0)), s(mark(z0)))), MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons1(mark(z0), mark(z1)))), MARK(cons1(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), s(z0))) -> c2(A__2ND(cons1(a__from(mark(x0)), s(mark(z0)))), MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons1(mark(z0), mark(z1)))), MARK(cons1(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), s(z0))) -> c2(A__2ND(cons1(a__from(mark(x0)), s(mark(z0)))), MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons1(mark(z0), mark(z1)))), MARK(cons1(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (79) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__2ND(cons(cons(z0, z1), x1)) -> c2(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(x1)) by A__2ND(cons(cons(x0, x1), 2nd(z0))) -> c2(A__2ND(cons1(cons(mark(x0), x1), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(cons(x0, x1), from(z0))) -> c2(A__2ND(cons1(cons(mark(x0), x1), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(A__2ND(cons1(cons(mark(x0), x1), s(mark(z0)))), MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons1(mark(z0), mark(z1)))), MARK(cons1(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(A__2ND(cons1(cons(mark(x0), x1), s(mark(z0)))), MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons1(mark(z0), mark(z1)))), MARK(cons1(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(A__2ND(cons1(cons(mark(x0), x1), s(mark(z0)))), MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons1(mark(z0), mark(z1)))), MARK(cons1(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__2ND(cons(s(z0), x1)) -> c2(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(x1)) by A__2ND(cons(s(x0), 2nd(z0))) -> c2(A__2ND(cons1(s(mark(x0)), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(s(x0), from(z0))) -> c2(A__2ND(cons1(s(mark(x0)), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(x0), s(z0))) -> c2(A__2ND(cons1(s(mark(x0)), s(mark(z0)))), MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons1(mark(z0), mark(z1)))), MARK(cons1(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(x0), s(z0))) -> c2(A__2ND(cons1(s(mark(x0)), s(mark(z0)))), MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons1(mark(z0), mark(z1)))), MARK(cons1(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(x0), s(z0))) -> c2(A__2ND(cons1(s(mark(x0)), s(mark(z0)))), MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons1(mark(z0), mark(z1)))), MARK(cons1(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (87) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__2ND(cons(cons1(z0, z1), x1)) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(x1)) by A__2ND(cons(cons1(x0, x1), 2nd(z0))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), a__2nd(mark(z0)))), MARK(2nd(z0))) A__2ND(cons(cons1(x0, x1), from(z0))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), a__from(mark(z0)))), MARK(from(z0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), s(mark(z0)))), MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons1(mark(z0), mark(z1)))), MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), s(mark(z0)))), MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons1(mark(z0), mark(z1)))), MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), s(mark(z0)))), MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons1(mark(z0), mark(z1)))), MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (91) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (93) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(2nd(2nd(z0))) -> c6(A__2ND(a__2nd(mark(z0))), MARK(2nd(z0))) by MARK(2nd(2nd(x0))) -> c6(A__2ND(2nd(mark(x0))), MARK(2nd(x0))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(x0))) -> c6(A__2ND(2nd(mark(x0))), MARK(2nd(x0))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(x0))) -> c6(A__2ND(2nd(mark(x0))), MARK(2nd(x0))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (95) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (97) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(2nd(from(z0))) -> c6(A__2ND(a__from(mark(z0))), MARK(from(z0))) by MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(from(mark(x0))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(from(mark(x0))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(from(mark(x0))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (99) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (101) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(2nd(cons1(z0, z1))) -> c6(A__2ND(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) by MARK(2nd(cons1(x0, 2nd(z0)))) -> c6(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(cons1(x0, 2nd(z0)))) MARK(2nd(cons1(x0, from(z0)))) -> c6(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(cons1(x0, from(z0)))) MARK(2nd(cons1(x0, cons(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons1(x0, cons(z0, z1)))) MARK(2nd(cons1(x0, s(z0)))) -> c6(A__2ND(cons1(mark(x0), s(mark(z0)))), MARK(cons1(x0, s(z0)))) MARK(2nd(cons1(x0, cons1(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons1(mark(z0), mark(z1)))), MARK(cons1(x0, cons1(z0, z1)))) MARK(2nd(cons1(2nd(z0), x1))) -> c6(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(cons1(2nd(z0), x1))) MARK(2nd(cons1(from(z0), x1))) -> c6(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(cons1(from(z0), x1))) MARK(2nd(cons1(cons(z0, z1), x1))) -> c6(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons1(cons(z0, z1), x1))) MARK(2nd(cons1(s(z0), x1))) -> c6(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(cons1(s(z0), x1))) MARK(2nd(cons1(cons1(z0, z1), x1))) -> c6(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(cons1(z0, z1), x1))) MARK(2nd(cons1(x0, x1))) -> c6(MARK(cons1(x0, x1))) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) MARK(2nd(cons1(x0, 2nd(z0)))) -> c6(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(cons1(x0, 2nd(z0)))) MARK(2nd(cons1(x0, from(z0)))) -> c6(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(cons1(x0, from(z0)))) MARK(2nd(cons1(x0, cons(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons1(x0, cons(z0, z1)))) MARK(2nd(cons1(x0, s(z0)))) -> c6(A__2ND(cons1(mark(x0), s(mark(z0)))), MARK(cons1(x0, s(z0)))) MARK(2nd(cons1(x0, cons1(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons1(mark(z0), mark(z1)))), MARK(cons1(x0, cons1(z0, z1)))) MARK(2nd(cons1(2nd(z0), x1))) -> c6(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(cons1(2nd(z0), x1))) MARK(2nd(cons1(from(z0), x1))) -> c6(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(cons1(from(z0), x1))) MARK(2nd(cons1(cons(z0, z1), x1))) -> c6(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons1(cons(z0, z1), x1))) MARK(2nd(cons1(s(z0), x1))) -> c6(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(cons1(s(z0), x1))) MARK(2nd(cons1(cons1(z0, z1), x1))) -> c6(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(cons1(z0, z1), x1))) MARK(2nd(cons1(x0, x1))) -> c6(MARK(cons1(x0, x1))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) MARK(2nd(cons1(x0, 2nd(z0)))) -> c6(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(cons1(x0, 2nd(z0)))) MARK(2nd(cons1(x0, from(z0)))) -> c6(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(cons1(x0, from(z0)))) MARK(2nd(cons1(x0, cons(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons1(x0, cons(z0, z1)))) MARK(2nd(cons1(x0, s(z0)))) -> c6(A__2ND(cons1(mark(x0), s(mark(z0)))), MARK(cons1(x0, s(z0)))) MARK(2nd(cons1(x0, cons1(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons1(mark(z0), mark(z1)))), MARK(cons1(x0, cons1(z0, z1)))) MARK(2nd(cons1(2nd(z0), x1))) -> c6(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(cons1(2nd(z0), x1))) MARK(2nd(cons1(from(z0), x1))) -> c6(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(cons1(from(z0), x1))) MARK(2nd(cons1(cons(z0, z1), x1))) -> c6(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons1(cons(z0, z1), x1))) MARK(2nd(cons1(s(z0), x1))) -> c6(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(cons1(s(z0), x1))) MARK(2nd(cons1(cons1(z0, z1), x1))) -> c6(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(cons1(z0, z1), x1))) MARK(2nd(cons1(x0, x1))) -> c6(MARK(cons1(x0, x1))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (103) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) MARK(2nd(cons1(x0, 2nd(z0)))) -> c6(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(cons1(x0, 2nd(z0)))) MARK(2nd(cons1(x0, from(z0)))) -> c6(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(cons1(x0, from(z0)))) MARK(2nd(cons1(x0, cons(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons1(x0, cons(z0, z1)))) MARK(2nd(cons1(2nd(z0), x1))) -> c6(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(cons1(2nd(z0), x1))) MARK(2nd(cons1(from(z0), x1))) -> c6(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(cons1(from(z0), x1))) MARK(2nd(cons1(cons(z0, z1), x1))) -> c6(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons1(cons(z0, z1), x1))) MARK(2nd(cons1(s(z0), x1))) -> c6(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(cons1(s(z0), x1))) MARK(2nd(cons1(cons1(z0, z1), x1))) -> c6(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(cons1(z0, z1), x1))) MARK(2nd(cons1(x0, x1))) -> c6(MARK(cons1(x0, x1))) MARK(2nd(cons1(x0, s(z0)))) -> c6(MARK(cons1(x0, s(z0)))) MARK(2nd(cons1(x0, cons1(z0, z1)))) -> c6(MARK(cons1(x0, cons1(z0, z1)))) S tuples: A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) MARK(2nd(cons1(x0, 2nd(z0)))) -> c6(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(cons1(x0, 2nd(z0)))) MARK(2nd(cons1(x0, from(z0)))) -> c6(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(cons1(x0, from(z0)))) MARK(2nd(cons1(x0, cons(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons1(x0, cons(z0, z1)))) MARK(2nd(cons1(2nd(z0), x1))) -> c6(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(cons1(2nd(z0), x1))) MARK(2nd(cons1(from(z0), x1))) -> c6(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(cons1(from(z0), x1))) MARK(2nd(cons1(cons(z0, z1), x1))) -> c6(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons1(cons(z0, z1), x1))) MARK(2nd(cons1(s(z0), x1))) -> c6(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(cons1(s(z0), x1))) MARK(2nd(cons1(cons1(z0, z1), x1))) -> c6(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(cons1(z0, z1), x1))) MARK(2nd(cons1(x0, x1))) -> c6(MARK(cons1(x0, x1))) MARK(2nd(cons1(x0, s(z0)))) -> c6(MARK(cons1(x0, s(z0)))) MARK(2nd(cons1(x0, cons1(z0, z1)))) -> c6(MARK(cons1(x0, cons1(z0, z1)))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, A__FROM_1, MARK_1 Compound Symbols: c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1 ---------------------------------------- (105) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace A__2ND(cons1(z0, cons(z1, z2))) -> c(MARK(z1)) by A__2ND(cons1(z0, cons(from(y0), z2))) -> c(MARK(from(y0))) A__2ND(cons1(z0, cons(cons(y0, y1), z2))) -> c(MARK(cons(y0, y1))) A__2ND(cons1(z0, cons(s(y0), z2))) -> c(MARK(s(y0))) A__2ND(cons1(z0, cons(cons1(y0, y1), z2))) -> c(MARK(cons1(y0, y1))) A__2ND(cons1(z0, cons(2nd(cons(y0, y1)), z2))) -> c(MARK(2nd(cons(y0, y1)))) A__2ND(cons1(z0, cons(2nd(s(y0)), z2))) -> c(MARK(2nd(s(y0)))) A__2ND(cons1(z0, cons(2nd(2nd(2nd(y0))), z2))) -> c(MARK(2nd(2nd(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(from(y0))), z2))) -> c(MARK(2nd(2nd(from(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(s(y0))), z2))) -> c(MARK(2nd(2nd(s(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons1(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(y0)), z2))) -> c(MARK(2nd(2nd(y0)))) A__2ND(cons1(z0, cons(2nd(from(y0)), z2))) -> c(MARK(2nd(from(y0)))) A__2ND(cons1(z0, cons(2nd(from(2nd(y0))), z2))) -> c(MARK(2nd(from(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(from(from(y0))), z2))) -> c(MARK(2nd(from(from(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons(y0, y1))), z2))) -> c(MARK(2nd(from(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(from(s(y0))), z2))) -> c(MARK(2nd(from(s(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons1(y0, y1))), z2))) -> c(MARK(2nd(from(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, 2nd(y1))), z2))) -> c(MARK(2nd(cons1(y0, 2nd(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, from(y1))), z2))) -> c(MARK(2nd(cons1(y0, from(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons(y1, y2))))) A__2ND(cons1(z0, cons(2nd(cons1(2nd(y0), y1)), z2))) -> c(MARK(2nd(cons1(2nd(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(from(y0), y1)), z2))) -> c(MARK(2nd(cons1(from(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(s(y0), y1)), z2))) -> c(MARK(2nd(cons1(s(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons1(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, y1)), z2))) -> c(MARK(2nd(cons1(y0, y1)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, s(y1))), z2))) -> c(MARK(2nd(cons1(y0, s(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons1(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons1(y1, y2))))) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) MARK(2nd(cons1(x0, 2nd(z0)))) -> c6(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(cons1(x0, 2nd(z0)))) MARK(2nd(cons1(x0, from(z0)))) -> c6(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(cons1(x0, from(z0)))) MARK(2nd(cons1(x0, cons(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons1(x0, cons(z0, z1)))) MARK(2nd(cons1(2nd(z0), x1))) -> c6(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(cons1(2nd(z0), x1))) MARK(2nd(cons1(from(z0), x1))) -> c6(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(cons1(from(z0), x1))) MARK(2nd(cons1(cons(z0, z1), x1))) -> c6(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons1(cons(z0, z1), x1))) MARK(2nd(cons1(s(z0), x1))) -> c6(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(cons1(s(z0), x1))) MARK(2nd(cons1(cons1(z0, z1), x1))) -> c6(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(cons1(z0, z1), x1))) MARK(2nd(cons1(x0, x1))) -> c6(MARK(cons1(x0, x1))) MARK(2nd(cons1(x0, s(z0)))) -> c6(MARK(cons1(x0, s(z0)))) MARK(2nd(cons1(x0, cons1(z0, z1)))) -> c6(MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons1(z0, cons(from(y0), z2))) -> c(MARK(from(y0))) A__2ND(cons1(z0, cons(cons(y0, y1), z2))) -> c(MARK(cons(y0, y1))) A__2ND(cons1(z0, cons(s(y0), z2))) -> c(MARK(s(y0))) A__2ND(cons1(z0, cons(cons1(y0, y1), z2))) -> c(MARK(cons1(y0, y1))) A__2ND(cons1(z0, cons(2nd(cons(y0, y1)), z2))) -> c(MARK(2nd(cons(y0, y1)))) A__2ND(cons1(z0, cons(2nd(s(y0)), z2))) -> c(MARK(2nd(s(y0)))) A__2ND(cons1(z0, cons(2nd(2nd(2nd(y0))), z2))) -> c(MARK(2nd(2nd(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(from(y0))), z2))) -> c(MARK(2nd(2nd(from(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(s(y0))), z2))) -> c(MARK(2nd(2nd(s(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons1(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(y0)), z2))) -> c(MARK(2nd(2nd(y0)))) A__2ND(cons1(z0, cons(2nd(from(y0)), z2))) -> c(MARK(2nd(from(y0)))) A__2ND(cons1(z0, cons(2nd(from(2nd(y0))), z2))) -> c(MARK(2nd(from(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(from(from(y0))), z2))) -> c(MARK(2nd(from(from(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons(y0, y1))), z2))) -> c(MARK(2nd(from(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(from(s(y0))), z2))) -> c(MARK(2nd(from(s(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons1(y0, y1))), z2))) -> c(MARK(2nd(from(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, 2nd(y1))), z2))) -> c(MARK(2nd(cons1(y0, 2nd(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, from(y1))), z2))) -> c(MARK(2nd(cons1(y0, from(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons(y1, y2))))) A__2ND(cons1(z0, cons(2nd(cons1(2nd(y0), y1)), z2))) -> c(MARK(2nd(cons1(2nd(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(from(y0), y1)), z2))) -> c(MARK(2nd(cons1(from(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(s(y0), y1)), z2))) -> c(MARK(2nd(cons1(s(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons1(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, y1)), z2))) -> c(MARK(2nd(cons1(y0, y1)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, s(y1))), z2))) -> c(MARK(2nd(cons1(y0, s(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons1(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons1(y1, y2))))) S tuples: A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) MARK(2nd(cons1(x0, 2nd(z0)))) -> c6(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(cons1(x0, 2nd(z0)))) MARK(2nd(cons1(x0, from(z0)))) -> c6(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(cons1(x0, from(z0)))) MARK(2nd(cons1(x0, cons(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons1(x0, cons(z0, z1)))) MARK(2nd(cons1(2nd(z0), x1))) -> c6(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(cons1(2nd(z0), x1))) MARK(2nd(cons1(from(z0), x1))) -> c6(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(cons1(from(z0), x1))) MARK(2nd(cons1(cons(z0, z1), x1))) -> c6(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons1(cons(z0, z1), x1))) MARK(2nd(cons1(s(z0), x1))) -> c6(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(cons1(s(z0), x1))) MARK(2nd(cons1(cons1(z0, z1), x1))) -> c6(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(cons1(z0, z1), x1))) MARK(2nd(cons1(x0, x1))) -> c6(MARK(cons1(x0, x1))) MARK(2nd(cons1(x0, s(z0)))) -> c6(MARK(cons1(x0, s(z0)))) MARK(2nd(cons1(x0, cons1(z0, z1)))) -> c6(MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons1(z0, cons(from(y0), z2))) -> c(MARK(from(y0))) A__2ND(cons1(z0, cons(cons(y0, y1), z2))) -> c(MARK(cons(y0, y1))) A__2ND(cons1(z0, cons(s(y0), z2))) -> c(MARK(s(y0))) A__2ND(cons1(z0, cons(cons1(y0, y1), z2))) -> c(MARK(cons1(y0, y1))) A__2ND(cons1(z0, cons(2nd(cons(y0, y1)), z2))) -> c(MARK(2nd(cons(y0, y1)))) A__2ND(cons1(z0, cons(2nd(s(y0)), z2))) -> c(MARK(2nd(s(y0)))) A__2ND(cons1(z0, cons(2nd(2nd(2nd(y0))), z2))) -> c(MARK(2nd(2nd(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(from(y0))), z2))) -> c(MARK(2nd(2nd(from(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(s(y0))), z2))) -> c(MARK(2nd(2nd(s(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons1(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(y0)), z2))) -> c(MARK(2nd(2nd(y0)))) A__2ND(cons1(z0, cons(2nd(from(y0)), z2))) -> c(MARK(2nd(from(y0)))) A__2ND(cons1(z0, cons(2nd(from(2nd(y0))), z2))) -> c(MARK(2nd(from(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(from(from(y0))), z2))) -> c(MARK(2nd(from(from(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons(y0, y1))), z2))) -> c(MARK(2nd(from(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(from(s(y0))), z2))) -> c(MARK(2nd(from(s(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons1(y0, y1))), z2))) -> c(MARK(2nd(from(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, 2nd(y1))), z2))) -> c(MARK(2nd(cons1(y0, 2nd(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, from(y1))), z2))) -> c(MARK(2nd(cons1(y0, from(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons(y1, y2))))) A__2ND(cons1(z0, cons(2nd(cons1(2nd(y0), y1)), z2))) -> c(MARK(2nd(cons1(2nd(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(from(y0), y1)), z2))) -> c(MARK(2nd(cons1(from(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(s(y0), y1)), z2))) -> c(MARK(2nd(cons1(s(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons1(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, y1)), z2))) -> c(MARK(2nd(cons1(y0, y1)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, s(y1))), z2))) -> c(MARK(2nd(cons1(y0, s(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons1(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons1(y1, y2))))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__FROM_1, MARK_1, A__2ND_1 Compound Symbols: c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_2, c1_1, c2_2, c2_1, c6_2, c6_1, c_1 ---------------------------------------- (107) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__2ND(cons(x0, cons(z0, z1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(x0)) by A__2ND(cons(x0, cons(2nd(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(from(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(x0)) A__2ND(cons(x0, cons(s(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(x0)) A__2ND(cons(2nd(z0), cons(x1, x2))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), cons(mark(x1), x2))), MARK(2nd(z0))) A__2ND(cons(from(z0), cons(x1, x2))) -> c1(A__2ND(cons1(a__from(mark(z0)), cons(mark(x1), x2))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), cons(x1, x2))) -> c1(A__2ND(cons1(cons(mark(z0), z1), cons(mark(x1), x2))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), cons(x1, x2))) -> c1(A__2ND(cons1(s(mark(z0)), cons(mark(x1), x2))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), cons(x1, x2))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), cons(mark(x1), x2))), MARK(cons1(z0, z1))) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) MARK(2nd(cons1(x0, 2nd(z0)))) -> c6(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(cons1(x0, 2nd(z0)))) MARK(2nd(cons1(x0, from(z0)))) -> c6(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(cons1(x0, from(z0)))) MARK(2nd(cons1(x0, cons(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons1(x0, cons(z0, z1)))) MARK(2nd(cons1(2nd(z0), x1))) -> c6(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(cons1(2nd(z0), x1))) MARK(2nd(cons1(from(z0), x1))) -> c6(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(cons1(from(z0), x1))) MARK(2nd(cons1(cons(z0, z1), x1))) -> c6(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons1(cons(z0, z1), x1))) MARK(2nd(cons1(s(z0), x1))) -> c6(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(cons1(s(z0), x1))) MARK(2nd(cons1(cons1(z0, z1), x1))) -> c6(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(cons1(z0, z1), x1))) MARK(2nd(cons1(x0, x1))) -> c6(MARK(cons1(x0, x1))) MARK(2nd(cons1(x0, s(z0)))) -> c6(MARK(cons1(x0, s(z0)))) MARK(2nd(cons1(x0, cons1(z0, z1)))) -> c6(MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons1(z0, cons(from(y0), z2))) -> c(MARK(from(y0))) A__2ND(cons1(z0, cons(cons(y0, y1), z2))) -> c(MARK(cons(y0, y1))) A__2ND(cons1(z0, cons(s(y0), z2))) -> c(MARK(s(y0))) A__2ND(cons1(z0, cons(cons1(y0, y1), z2))) -> c(MARK(cons1(y0, y1))) A__2ND(cons1(z0, cons(2nd(cons(y0, y1)), z2))) -> c(MARK(2nd(cons(y0, y1)))) A__2ND(cons1(z0, cons(2nd(s(y0)), z2))) -> c(MARK(2nd(s(y0)))) A__2ND(cons1(z0, cons(2nd(2nd(2nd(y0))), z2))) -> c(MARK(2nd(2nd(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(from(y0))), z2))) -> c(MARK(2nd(2nd(from(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(s(y0))), z2))) -> c(MARK(2nd(2nd(s(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons1(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(y0)), z2))) -> c(MARK(2nd(2nd(y0)))) A__2ND(cons1(z0, cons(2nd(from(y0)), z2))) -> c(MARK(2nd(from(y0)))) A__2ND(cons1(z0, cons(2nd(from(2nd(y0))), z2))) -> c(MARK(2nd(from(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(from(from(y0))), z2))) -> c(MARK(2nd(from(from(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons(y0, y1))), z2))) -> c(MARK(2nd(from(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(from(s(y0))), z2))) -> c(MARK(2nd(from(s(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons1(y0, y1))), z2))) -> c(MARK(2nd(from(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, 2nd(y1))), z2))) -> c(MARK(2nd(cons1(y0, 2nd(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, from(y1))), z2))) -> c(MARK(2nd(cons1(y0, from(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons(y1, y2))))) A__2ND(cons1(z0, cons(2nd(cons1(2nd(y0), y1)), z2))) -> c(MARK(2nd(cons1(2nd(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(from(y0), y1)), z2))) -> c(MARK(2nd(cons1(from(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(s(y0), y1)), z2))) -> c(MARK(2nd(cons1(s(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons1(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, y1)), z2))) -> c(MARK(2nd(cons1(y0, y1)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, s(y1))), z2))) -> c(MARK(2nd(cons1(y0, s(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons1(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons1(y1, y2))))) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(from(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(x0)) A__2ND(cons(x0, cons(s(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(x0)) S tuples: A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) MARK(2nd(cons1(x0, 2nd(z0)))) -> c6(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(cons1(x0, 2nd(z0)))) MARK(2nd(cons1(x0, from(z0)))) -> c6(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(cons1(x0, from(z0)))) MARK(2nd(cons1(x0, cons(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons1(x0, cons(z0, z1)))) MARK(2nd(cons1(2nd(z0), x1))) -> c6(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(cons1(2nd(z0), x1))) MARK(2nd(cons1(from(z0), x1))) -> c6(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(cons1(from(z0), x1))) MARK(2nd(cons1(cons(z0, z1), x1))) -> c6(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons1(cons(z0, z1), x1))) MARK(2nd(cons1(s(z0), x1))) -> c6(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(cons1(s(z0), x1))) MARK(2nd(cons1(cons1(z0, z1), x1))) -> c6(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(cons1(z0, z1), x1))) MARK(2nd(cons1(x0, x1))) -> c6(MARK(cons1(x0, x1))) MARK(2nd(cons1(x0, s(z0)))) -> c6(MARK(cons1(x0, s(z0)))) MARK(2nd(cons1(x0, cons1(z0, z1)))) -> c6(MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons1(z0, cons(from(y0), z2))) -> c(MARK(from(y0))) A__2ND(cons1(z0, cons(cons(y0, y1), z2))) -> c(MARK(cons(y0, y1))) A__2ND(cons1(z0, cons(s(y0), z2))) -> c(MARK(s(y0))) A__2ND(cons1(z0, cons(cons1(y0, y1), z2))) -> c(MARK(cons1(y0, y1))) A__2ND(cons1(z0, cons(2nd(cons(y0, y1)), z2))) -> c(MARK(2nd(cons(y0, y1)))) A__2ND(cons1(z0, cons(2nd(s(y0)), z2))) -> c(MARK(2nd(s(y0)))) A__2ND(cons1(z0, cons(2nd(2nd(2nd(y0))), z2))) -> c(MARK(2nd(2nd(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(from(y0))), z2))) -> c(MARK(2nd(2nd(from(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(s(y0))), z2))) -> c(MARK(2nd(2nd(s(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons1(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(y0)), z2))) -> c(MARK(2nd(2nd(y0)))) A__2ND(cons1(z0, cons(2nd(from(y0)), z2))) -> c(MARK(2nd(from(y0)))) A__2ND(cons1(z0, cons(2nd(from(2nd(y0))), z2))) -> c(MARK(2nd(from(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(from(from(y0))), z2))) -> c(MARK(2nd(from(from(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons(y0, y1))), z2))) -> c(MARK(2nd(from(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(from(s(y0))), z2))) -> c(MARK(2nd(from(s(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons1(y0, y1))), z2))) -> c(MARK(2nd(from(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, 2nd(y1))), z2))) -> c(MARK(2nd(cons1(y0, 2nd(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, from(y1))), z2))) -> c(MARK(2nd(cons1(y0, from(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons(y1, y2))))) A__2ND(cons1(z0, cons(2nd(cons1(2nd(y0), y1)), z2))) -> c(MARK(2nd(cons1(2nd(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(from(y0), y1)), z2))) -> c(MARK(2nd(cons1(from(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(s(y0), y1)), z2))) -> c(MARK(2nd(cons1(s(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons1(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, y1)), z2))) -> c(MARK(2nd(cons1(y0, y1)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, s(y1))), z2))) -> c(MARK(2nd(cons1(y0, s(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons1(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons1(y1, y2))))) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(from(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(x0)) A__2ND(cons(x0, cons(s(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(x0)) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__FROM_1, MARK_1, A__2ND_1 Compound Symbols: c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_1, c2_2, c2_1, c6_2, c6_1, c1_2, c_1 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__2ND(cons(x0, cons(z0, z1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons(z0, z1))) by A__2ND(cons(x0, cons(2nd(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(cons(2nd(z0), x2))) A__2ND(cons(x0, cons(from(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(cons(from(z0), x2))) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(cons(cons(z0, z1), x2))) A__2ND(cons(x0, cons(s(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(cons(s(z0), x2))) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(cons(cons1(z0, z1), x2))) A__2ND(cons(2nd(z0), cons(x1, x2))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), cons(mark(x1), x2))), MARK(cons(x1, x2))) A__2ND(cons(from(z0), cons(x1, x2))) -> c2(A__2ND(cons1(a__from(mark(z0)), cons(mark(x1), x2))), MARK(cons(x1, x2))) A__2ND(cons(cons(z0, z1), cons(x1, x2))) -> c2(A__2ND(cons1(cons(mark(z0), z1), cons(mark(x1), x2))), MARK(cons(x1, x2))) A__2ND(cons(s(z0), cons(x1, x2))) -> c2(A__2ND(cons1(s(mark(z0)), cons(mark(x1), x2))), MARK(cons(x1, x2))) A__2ND(cons(cons1(z0, z1), cons(x1, x2))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), cons(mark(x1), x2))), MARK(cons(x1, x2))) A__2ND(cons(x0, cons(x1, x2))) -> c2(MARK(cons(x1, x2))) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) MARK(2nd(cons1(x0, 2nd(z0)))) -> c6(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(cons1(x0, 2nd(z0)))) MARK(2nd(cons1(x0, from(z0)))) -> c6(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(cons1(x0, from(z0)))) MARK(2nd(cons1(x0, cons(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons1(x0, cons(z0, z1)))) MARK(2nd(cons1(2nd(z0), x1))) -> c6(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(cons1(2nd(z0), x1))) MARK(2nd(cons1(from(z0), x1))) -> c6(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(cons1(from(z0), x1))) MARK(2nd(cons1(cons(z0, z1), x1))) -> c6(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons1(cons(z0, z1), x1))) MARK(2nd(cons1(s(z0), x1))) -> c6(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(cons1(s(z0), x1))) MARK(2nd(cons1(cons1(z0, z1), x1))) -> c6(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(cons1(z0, z1), x1))) MARK(2nd(cons1(x0, x1))) -> c6(MARK(cons1(x0, x1))) MARK(2nd(cons1(x0, s(z0)))) -> c6(MARK(cons1(x0, s(z0)))) MARK(2nd(cons1(x0, cons1(z0, z1)))) -> c6(MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons1(z0, cons(from(y0), z2))) -> c(MARK(from(y0))) A__2ND(cons1(z0, cons(cons(y0, y1), z2))) -> c(MARK(cons(y0, y1))) A__2ND(cons1(z0, cons(s(y0), z2))) -> c(MARK(s(y0))) A__2ND(cons1(z0, cons(cons1(y0, y1), z2))) -> c(MARK(cons1(y0, y1))) A__2ND(cons1(z0, cons(2nd(cons(y0, y1)), z2))) -> c(MARK(2nd(cons(y0, y1)))) A__2ND(cons1(z0, cons(2nd(s(y0)), z2))) -> c(MARK(2nd(s(y0)))) A__2ND(cons1(z0, cons(2nd(2nd(2nd(y0))), z2))) -> c(MARK(2nd(2nd(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(from(y0))), z2))) -> c(MARK(2nd(2nd(from(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(s(y0))), z2))) -> c(MARK(2nd(2nd(s(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons1(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(y0)), z2))) -> c(MARK(2nd(2nd(y0)))) A__2ND(cons1(z0, cons(2nd(from(y0)), z2))) -> c(MARK(2nd(from(y0)))) A__2ND(cons1(z0, cons(2nd(from(2nd(y0))), z2))) -> c(MARK(2nd(from(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(from(from(y0))), z2))) -> c(MARK(2nd(from(from(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons(y0, y1))), z2))) -> c(MARK(2nd(from(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(from(s(y0))), z2))) -> c(MARK(2nd(from(s(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons1(y0, y1))), z2))) -> c(MARK(2nd(from(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, 2nd(y1))), z2))) -> c(MARK(2nd(cons1(y0, 2nd(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, from(y1))), z2))) -> c(MARK(2nd(cons1(y0, from(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons(y1, y2))))) A__2ND(cons1(z0, cons(2nd(cons1(2nd(y0), y1)), z2))) -> c(MARK(2nd(cons1(2nd(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(from(y0), y1)), z2))) -> c(MARK(2nd(cons1(from(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(s(y0), y1)), z2))) -> c(MARK(2nd(cons1(s(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons1(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, y1)), z2))) -> c(MARK(2nd(cons1(y0, y1)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, s(y1))), z2))) -> c(MARK(2nd(cons1(y0, s(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons1(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons1(y1, y2))))) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(from(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(x0)) A__2ND(cons(x0, cons(s(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(x0)) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(cons(2nd(z0), x2))) A__2ND(cons(x0, cons(from(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(cons(from(z0), x2))) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(cons(cons(z0, z1), x2))) A__2ND(cons(x0, cons(s(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(cons(s(z0), x2))) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(cons(cons1(z0, z1), x2))) A__2ND(cons(x0, cons(x1, x2))) -> c2(MARK(cons(x1, x2))) S tuples: A__FROM(z0) -> c4(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) MARK(2nd(cons1(x0, 2nd(z0)))) -> c6(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(cons1(x0, 2nd(z0)))) MARK(2nd(cons1(x0, from(z0)))) -> c6(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(cons1(x0, from(z0)))) MARK(2nd(cons1(x0, cons(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons1(x0, cons(z0, z1)))) MARK(2nd(cons1(2nd(z0), x1))) -> c6(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(cons1(2nd(z0), x1))) MARK(2nd(cons1(from(z0), x1))) -> c6(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(cons1(from(z0), x1))) MARK(2nd(cons1(cons(z0, z1), x1))) -> c6(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons1(cons(z0, z1), x1))) MARK(2nd(cons1(s(z0), x1))) -> c6(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(cons1(s(z0), x1))) MARK(2nd(cons1(cons1(z0, z1), x1))) -> c6(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(cons1(z0, z1), x1))) MARK(2nd(cons1(x0, x1))) -> c6(MARK(cons1(x0, x1))) MARK(2nd(cons1(x0, s(z0)))) -> c6(MARK(cons1(x0, s(z0)))) MARK(2nd(cons1(x0, cons1(z0, z1)))) -> c6(MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons1(z0, cons(from(y0), z2))) -> c(MARK(from(y0))) A__2ND(cons1(z0, cons(cons(y0, y1), z2))) -> c(MARK(cons(y0, y1))) A__2ND(cons1(z0, cons(s(y0), z2))) -> c(MARK(s(y0))) A__2ND(cons1(z0, cons(cons1(y0, y1), z2))) -> c(MARK(cons1(y0, y1))) A__2ND(cons1(z0, cons(2nd(cons(y0, y1)), z2))) -> c(MARK(2nd(cons(y0, y1)))) A__2ND(cons1(z0, cons(2nd(s(y0)), z2))) -> c(MARK(2nd(s(y0)))) A__2ND(cons1(z0, cons(2nd(2nd(2nd(y0))), z2))) -> c(MARK(2nd(2nd(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(from(y0))), z2))) -> c(MARK(2nd(2nd(from(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(s(y0))), z2))) -> c(MARK(2nd(2nd(s(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons1(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(y0)), z2))) -> c(MARK(2nd(2nd(y0)))) A__2ND(cons1(z0, cons(2nd(from(y0)), z2))) -> c(MARK(2nd(from(y0)))) A__2ND(cons1(z0, cons(2nd(from(2nd(y0))), z2))) -> c(MARK(2nd(from(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(from(from(y0))), z2))) -> c(MARK(2nd(from(from(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons(y0, y1))), z2))) -> c(MARK(2nd(from(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(from(s(y0))), z2))) -> c(MARK(2nd(from(s(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons1(y0, y1))), z2))) -> c(MARK(2nd(from(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, 2nd(y1))), z2))) -> c(MARK(2nd(cons1(y0, 2nd(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, from(y1))), z2))) -> c(MARK(2nd(cons1(y0, from(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons(y1, y2))))) A__2ND(cons1(z0, cons(2nd(cons1(2nd(y0), y1)), z2))) -> c(MARK(2nd(cons1(2nd(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(from(y0), y1)), z2))) -> c(MARK(2nd(cons1(from(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(s(y0), y1)), z2))) -> c(MARK(2nd(cons1(s(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons1(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, y1)), z2))) -> c(MARK(2nd(cons1(y0, y1)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, s(y1))), z2))) -> c(MARK(2nd(cons1(y0, s(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons1(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons1(y1, y2))))) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(from(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(x0)) A__2ND(cons(x0, cons(s(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(x0)) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(cons(2nd(z0), x2))) A__2ND(cons(x0, cons(from(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(cons(from(z0), x2))) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(cons(cons(z0, z1), x2))) A__2ND(cons(x0, cons(s(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(cons(s(z0), x2))) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(cons(cons1(z0, z1), x2))) A__2ND(cons(x0, cons(x1, x2))) -> c2(MARK(cons(x1, x2))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__FROM_1, MARK_1, A__2ND_1 Compound Symbols: c4_1, c7_2, c8_1, c9_1, c10_1, c11_1, c1_1, c2_1, c6_2, c6_1, c1_2, c2_2, c_1 ---------------------------------------- (111) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace A__FROM(z0) -> c4(MARK(z0)) by A__FROM(from(y0)) -> c4(MARK(from(y0))) A__FROM(cons(y0, y1)) -> c4(MARK(cons(y0, y1))) A__FROM(s(y0)) -> c4(MARK(s(y0))) A__FROM(cons1(y0, y1)) -> c4(MARK(cons1(y0, y1))) A__FROM(2nd(cons(y0, y1))) -> c4(MARK(2nd(cons(y0, y1)))) A__FROM(2nd(s(y0))) -> c4(MARK(2nd(s(y0)))) A__FROM(2nd(2nd(2nd(y0)))) -> c4(MARK(2nd(2nd(2nd(y0))))) A__FROM(2nd(2nd(from(y0)))) -> c4(MARK(2nd(2nd(from(y0))))) A__FROM(2nd(2nd(cons(y0, y1)))) -> c4(MARK(2nd(2nd(cons(y0, y1))))) A__FROM(2nd(2nd(s(y0)))) -> c4(MARK(2nd(2nd(s(y0))))) A__FROM(2nd(2nd(cons1(y0, y1)))) -> c4(MARK(2nd(2nd(cons1(y0, y1))))) A__FROM(2nd(2nd(y0))) -> c4(MARK(2nd(2nd(y0)))) A__FROM(2nd(from(y0))) -> c4(MARK(2nd(from(y0)))) A__FROM(2nd(from(2nd(y0)))) -> c4(MARK(2nd(from(2nd(y0))))) A__FROM(2nd(from(from(y0)))) -> c4(MARK(2nd(from(from(y0))))) A__FROM(2nd(from(cons(y0, y1)))) -> c4(MARK(2nd(from(cons(y0, y1))))) A__FROM(2nd(from(s(y0)))) -> c4(MARK(2nd(from(s(y0))))) A__FROM(2nd(from(cons1(y0, y1)))) -> c4(MARK(2nd(from(cons1(y0, y1))))) A__FROM(2nd(cons1(y0, 2nd(y1)))) -> c4(MARK(2nd(cons1(y0, 2nd(y1))))) A__FROM(2nd(cons1(y0, from(y1)))) -> c4(MARK(2nd(cons1(y0, from(y1))))) A__FROM(2nd(cons1(y0, cons(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons(y1, y2))))) A__FROM(2nd(cons1(2nd(y0), y1))) -> c4(MARK(2nd(cons1(2nd(y0), y1)))) A__FROM(2nd(cons1(from(y0), y1))) -> c4(MARK(2nd(cons1(from(y0), y1)))) A__FROM(2nd(cons1(cons(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons(y0, y1), y2)))) A__FROM(2nd(cons1(s(y0), y1))) -> c4(MARK(2nd(cons1(s(y0), y1)))) A__FROM(2nd(cons1(cons1(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__FROM(2nd(cons1(y0, y1))) -> c4(MARK(2nd(cons1(y0, y1)))) A__FROM(2nd(cons1(y0, s(y1)))) -> c4(MARK(2nd(cons1(y0, s(y1))))) A__FROM(2nd(cons1(y0, cons1(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons1(y1, y2))))) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) MARK(2nd(cons1(x0, 2nd(z0)))) -> c6(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(cons1(x0, 2nd(z0)))) MARK(2nd(cons1(x0, from(z0)))) -> c6(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(cons1(x0, from(z0)))) MARK(2nd(cons1(x0, cons(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons1(x0, cons(z0, z1)))) MARK(2nd(cons1(2nd(z0), x1))) -> c6(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(cons1(2nd(z0), x1))) MARK(2nd(cons1(from(z0), x1))) -> c6(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(cons1(from(z0), x1))) MARK(2nd(cons1(cons(z0, z1), x1))) -> c6(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons1(cons(z0, z1), x1))) MARK(2nd(cons1(s(z0), x1))) -> c6(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(cons1(s(z0), x1))) MARK(2nd(cons1(cons1(z0, z1), x1))) -> c6(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(cons1(z0, z1), x1))) MARK(2nd(cons1(x0, x1))) -> c6(MARK(cons1(x0, x1))) MARK(2nd(cons1(x0, s(z0)))) -> c6(MARK(cons1(x0, s(z0)))) MARK(2nd(cons1(x0, cons1(z0, z1)))) -> c6(MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons1(z0, cons(from(y0), z2))) -> c(MARK(from(y0))) A__2ND(cons1(z0, cons(cons(y0, y1), z2))) -> c(MARK(cons(y0, y1))) A__2ND(cons1(z0, cons(s(y0), z2))) -> c(MARK(s(y0))) A__2ND(cons1(z0, cons(cons1(y0, y1), z2))) -> c(MARK(cons1(y0, y1))) A__2ND(cons1(z0, cons(2nd(cons(y0, y1)), z2))) -> c(MARK(2nd(cons(y0, y1)))) A__2ND(cons1(z0, cons(2nd(s(y0)), z2))) -> c(MARK(2nd(s(y0)))) A__2ND(cons1(z0, cons(2nd(2nd(2nd(y0))), z2))) -> c(MARK(2nd(2nd(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(from(y0))), z2))) -> c(MARK(2nd(2nd(from(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(s(y0))), z2))) -> c(MARK(2nd(2nd(s(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons1(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(y0)), z2))) -> c(MARK(2nd(2nd(y0)))) A__2ND(cons1(z0, cons(2nd(from(y0)), z2))) -> c(MARK(2nd(from(y0)))) A__2ND(cons1(z0, cons(2nd(from(2nd(y0))), z2))) -> c(MARK(2nd(from(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(from(from(y0))), z2))) -> c(MARK(2nd(from(from(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons(y0, y1))), z2))) -> c(MARK(2nd(from(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(from(s(y0))), z2))) -> c(MARK(2nd(from(s(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons1(y0, y1))), z2))) -> c(MARK(2nd(from(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, 2nd(y1))), z2))) -> c(MARK(2nd(cons1(y0, 2nd(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, from(y1))), z2))) -> c(MARK(2nd(cons1(y0, from(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons(y1, y2))))) A__2ND(cons1(z0, cons(2nd(cons1(2nd(y0), y1)), z2))) -> c(MARK(2nd(cons1(2nd(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(from(y0), y1)), z2))) -> c(MARK(2nd(cons1(from(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(s(y0), y1)), z2))) -> c(MARK(2nd(cons1(s(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons1(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, y1)), z2))) -> c(MARK(2nd(cons1(y0, y1)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, s(y1))), z2))) -> c(MARK(2nd(cons1(y0, s(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons1(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons1(y1, y2))))) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(from(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(x0)) A__2ND(cons(x0, cons(s(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(x0)) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(cons(2nd(z0), x2))) A__2ND(cons(x0, cons(from(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(cons(from(z0), x2))) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(cons(cons(z0, z1), x2))) A__2ND(cons(x0, cons(s(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(cons(s(z0), x2))) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(cons(cons1(z0, z1), x2))) A__2ND(cons(x0, cons(x1, x2))) -> c2(MARK(cons(x1, x2))) A__FROM(from(y0)) -> c4(MARK(from(y0))) A__FROM(cons(y0, y1)) -> c4(MARK(cons(y0, y1))) A__FROM(s(y0)) -> c4(MARK(s(y0))) A__FROM(cons1(y0, y1)) -> c4(MARK(cons1(y0, y1))) A__FROM(2nd(cons(y0, y1))) -> c4(MARK(2nd(cons(y0, y1)))) A__FROM(2nd(s(y0))) -> c4(MARK(2nd(s(y0)))) A__FROM(2nd(2nd(2nd(y0)))) -> c4(MARK(2nd(2nd(2nd(y0))))) A__FROM(2nd(2nd(from(y0)))) -> c4(MARK(2nd(2nd(from(y0))))) A__FROM(2nd(2nd(cons(y0, y1)))) -> c4(MARK(2nd(2nd(cons(y0, y1))))) A__FROM(2nd(2nd(s(y0)))) -> c4(MARK(2nd(2nd(s(y0))))) A__FROM(2nd(2nd(cons1(y0, y1)))) -> c4(MARK(2nd(2nd(cons1(y0, y1))))) A__FROM(2nd(2nd(y0))) -> c4(MARK(2nd(2nd(y0)))) A__FROM(2nd(from(y0))) -> c4(MARK(2nd(from(y0)))) A__FROM(2nd(from(2nd(y0)))) -> c4(MARK(2nd(from(2nd(y0))))) A__FROM(2nd(from(from(y0)))) -> c4(MARK(2nd(from(from(y0))))) A__FROM(2nd(from(cons(y0, y1)))) -> c4(MARK(2nd(from(cons(y0, y1))))) A__FROM(2nd(from(s(y0)))) -> c4(MARK(2nd(from(s(y0))))) A__FROM(2nd(from(cons1(y0, y1)))) -> c4(MARK(2nd(from(cons1(y0, y1))))) A__FROM(2nd(cons1(y0, 2nd(y1)))) -> c4(MARK(2nd(cons1(y0, 2nd(y1))))) A__FROM(2nd(cons1(y0, from(y1)))) -> c4(MARK(2nd(cons1(y0, from(y1))))) A__FROM(2nd(cons1(y0, cons(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons(y1, y2))))) A__FROM(2nd(cons1(2nd(y0), y1))) -> c4(MARK(2nd(cons1(2nd(y0), y1)))) A__FROM(2nd(cons1(from(y0), y1))) -> c4(MARK(2nd(cons1(from(y0), y1)))) A__FROM(2nd(cons1(cons(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons(y0, y1), y2)))) A__FROM(2nd(cons1(s(y0), y1))) -> c4(MARK(2nd(cons1(s(y0), y1)))) A__FROM(2nd(cons1(cons1(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__FROM(2nd(cons1(y0, y1))) -> c4(MARK(2nd(cons1(y0, y1)))) A__FROM(2nd(cons1(y0, s(y1)))) -> c4(MARK(2nd(cons1(y0, s(y1))))) A__FROM(2nd(cons1(y0, cons1(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons1(y1, y2))))) S tuples: MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) MARK(2nd(cons1(x0, 2nd(z0)))) -> c6(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(cons1(x0, 2nd(z0)))) MARK(2nd(cons1(x0, from(z0)))) -> c6(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(cons1(x0, from(z0)))) MARK(2nd(cons1(x0, cons(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons1(x0, cons(z0, z1)))) MARK(2nd(cons1(2nd(z0), x1))) -> c6(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(cons1(2nd(z0), x1))) MARK(2nd(cons1(from(z0), x1))) -> c6(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(cons1(from(z0), x1))) MARK(2nd(cons1(cons(z0, z1), x1))) -> c6(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons1(cons(z0, z1), x1))) MARK(2nd(cons1(s(z0), x1))) -> c6(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(cons1(s(z0), x1))) MARK(2nd(cons1(cons1(z0, z1), x1))) -> c6(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(cons1(z0, z1), x1))) MARK(2nd(cons1(x0, x1))) -> c6(MARK(cons1(x0, x1))) MARK(2nd(cons1(x0, s(z0)))) -> c6(MARK(cons1(x0, s(z0)))) MARK(2nd(cons1(x0, cons1(z0, z1)))) -> c6(MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons1(z0, cons(from(y0), z2))) -> c(MARK(from(y0))) A__2ND(cons1(z0, cons(cons(y0, y1), z2))) -> c(MARK(cons(y0, y1))) A__2ND(cons1(z0, cons(s(y0), z2))) -> c(MARK(s(y0))) A__2ND(cons1(z0, cons(cons1(y0, y1), z2))) -> c(MARK(cons1(y0, y1))) A__2ND(cons1(z0, cons(2nd(cons(y0, y1)), z2))) -> c(MARK(2nd(cons(y0, y1)))) A__2ND(cons1(z0, cons(2nd(s(y0)), z2))) -> c(MARK(2nd(s(y0)))) A__2ND(cons1(z0, cons(2nd(2nd(2nd(y0))), z2))) -> c(MARK(2nd(2nd(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(from(y0))), z2))) -> c(MARK(2nd(2nd(from(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(s(y0))), z2))) -> c(MARK(2nd(2nd(s(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons1(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(y0)), z2))) -> c(MARK(2nd(2nd(y0)))) A__2ND(cons1(z0, cons(2nd(from(y0)), z2))) -> c(MARK(2nd(from(y0)))) A__2ND(cons1(z0, cons(2nd(from(2nd(y0))), z2))) -> c(MARK(2nd(from(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(from(from(y0))), z2))) -> c(MARK(2nd(from(from(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons(y0, y1))), z2))) -> c(MARK(2nd(from(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(from(s(y0))), z2))) -> c(MARK(2nd(from(s(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons1(y0, y1))), z2))) -> c(MARK(2nd(from(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, 2nd(y1))), z2))) -> c(MARK(2nd(cons1(y0, 2nd(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, from(y1))), z2))) -> c(MARK(2nd(cons1(y0, from(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons(y1, y2))))) A__2ND(cons1(z0, cons(2nd(cons1(2nd(y0), y1)), z2))) -> c(MARK(2nd(cons1(2nd(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(from(y0), y1)), z2))) -> c(MARK(2nd(cons1(from(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(s(y0), y1)), z2))) -> c(MARK(2nd(cons1(s(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons1(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, y1)), z2))) -> c(MARK(2nd(cons1(y0, y1)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, s(y1))), z2))) -> c(MARK(2nd(cons1(y0, s(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons1(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons1(y1, y2))))) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(from(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(x0)) A__2ND(cons(x0, cons(s(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(x0)) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(cons(2nd(z0), x2))) A__2ND(cons(x0, cons(from(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(cons(from(z0), x2))) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(cons(cons(z0, z1), x2))) A__2ND(cons(x0, cons(s(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(cons(s(z0), x2))) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(cons(cons1(z0, z1), x2))) A__2ND(cons(x0, cons(x1, x2))) -> c2(MARK(cons(x1, x2))) A__FROM(from(y0)) -> c4(MARK(from(y0))) A__FROM(cons(y0, y1)) -> c4(MARK(cons(y0, y1))) A__FROM(s(y0)) -> c4(MARK(s(y0))) A__FROM(cons1(y0, y1)) -> c4(MARK(cons1(y0, y1))) A__FROM(2nd(cons(y0, y1))) -> c4(MARK(2nd(cons(y0, y1)))) A__FROM(2nd(s(y0))) -> c4(MARK(2nd(s(y0)))) A__FROM(2nd(2nd(2nd(y0)))) -> c4(MARK(2nd(2nd(2nd(y0))))) A__FROM(2nd(2nd(from(y0)))) -> c4(MARK(2nd(2nd(from(y0))))) A__FROM(2nd(2nd(cons(y0, y1)))) -> c4(MARK(2nd(2nd(cons(y0, y1))))) A__FROM(2nd(2nd(s(y0)))) -> c4(MARK(2nd(2nd(s(y0))))) A__FROM(2nd(2nd(cons1(y0, y1)))) -> c4(MARK(2nd(2nd(cons1(y0, y1))))) A__FROM(2nd(2nd(y0))) -> c4(MARK(2nd(2nd(y0)))) A__FROM(2nd(from(y0))) -> c4(MARK(2nd(from(y0)))) A__FROM(2nd(from(2nd(y0)))) -> c4(MARK(2nd(from(2nd(y0))))) A__FROM(2nd(from(from(y0)))) -> c4(MARK(2nd(from(from(y0))))) A__FROM(2nd(from(cons(y0, y1)))) -> c4(MARK(2nd(from(cons(y0, y1))))) A__FROM(2nd(from(s(y0)))) -> c4(MARK(2nd(from(s(y0))))) A__FROM(2nd(from(cons1(y0, y1)))) -> c4(MARK(2nd(from(cons1(y0, y1))))) A__FROM(2nd(cons1(y0, 2nd(y1)))) -> c4(MARK(2nd(cons1(y0, 2nd(y1))))) A__FROM(2nd(cons1(y0, from(y1)))) -> c4(MARK(2nd(cons1(y0, from(y1))))) A__FROM(2nd(cons1(y0, cons(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons(y1, y2))))) A__FROM(2nd(cons1(2nd(y0), y1))) -> c4(MARK(2nd(cons1(2nd(y0), y1)))) A__FROM(2nd(cons1(from(y0), y1))) -> c4(MARK(2nd(cons1(from(y0), y1)))) A__FROM(2nd(cons1(cons(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons(y0, y1), y2)))) A__FROM(2nd(cons1(s(y0), y1))) -> c4(MARK(2nd(cons1(s(y0), y1)))) A__FROM(2nd(cons1(cons1(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__FROM(2nd(cons1(y0, y1))) -> c4(MARK(2nd(cons1(y0, y1)))) A__FROM(2nd(cons1(y0, s(y1)))) -> c4(MARK(2nd(cons1(y0, s(y1))))) A__FROM(2nd(cons1(y0, cons1(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons1(y1, y2))))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: MARK_1, A__2ND_1, A__FROM_1 Compound Symbols: c7_2, c8_1, c9_1, c10_1, c11_1, c1_1, c2_1, c6_2, c6_1, c1_2, c2_2, c_1, c4_1 ---------------------------------------- (113) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) by MARK(from(2nd(z0))) -> c7(A__FROM(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(from(from(z0))) -> c7(A__FROM(a__from(mark(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons1(z0, z1))) -> c7(A__FROM(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) MARK(2nd(cons1(x0, 2nd(z0)))) -> c6(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(cons1(x0, 2nd(z0)))) MARK(2nd(cons1(x0, from(z0)))) -> c6(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(cons1(x0, from(z0)))) MARK(2nd(cons1(x0, cons(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons1(x0, cons(z0, z1)))) MARK(2nd(cons1(2nd(z0), x1))) -> c6(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(cons1(2nd(z0), x1))) MARK(2nd(cons1(from(z0), x1))) -> c6(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(cons1(from(z0), x1))) MARK(2nd(cons1(cons(z0, z1), x1))) -> c6(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons1(cons(z0, z1), x1))) MARK(2nd(cons1(s(z0), x1))) -> c6(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(cons1(s(z0), x1))) MARK(2nd(cons1(cons1(z0, z1), x1))) -> c6(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(cons1(z0, z1), x1))) MARK(2nd(cons1(x0, x1))) -> c6(MARK(cons1(x0, x1))) MARK(2nd(cons1(x0, s(z0)))) -> c6(MARK(cons1(x0, s(z0)))) MARK(2nd(cons1(x0, cons1(z0, z1)))) -> c6(MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons1(z0, cons(from(y0), z2))) -> c(MARK(from(y0))) A__2ND(cons1(z0, cons(cons(y0, y1), z2))) -> c(MARK(cons(y0, y1))) A__2ND(cons1(z0, cons(s(y0), z2))) -> c(MARK(s(y0))) A__2ND(cons1(z0, cons(cons1(y0, y1), z2))) -> c(MARK(cons1(y0, y1))) A__2ND(cons1(z0, cons(2nd(cons(y0, y1)), z2))) -> c(MARK(2nd(cons(y0, y1)))) A__2ND(cons1(z0, cons(2nd(s(y0)), z2))) -> c(MARK(2nd(s(y0)))) A__2ND(cons1(z0, cons(2nd(2nd(2nd(y0))), z2))) -> c(MARK(2nd(2nd(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(from(y0))), z2))) -> c(MARK(2nd(2nd(from(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(s(y0))), z2))) -> c(MARK(2nd(2nd(s(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons1(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(y0)), z2))) -> c(MARK(2nd(2nd(y0)))) A__2ND(cons1(z0, cons(2nd(from(y0)), z2))) -> c(MARK(2nd(from(y0)))) A__2ND(cons1(z0, cons(2nd(from(2nd(y0))), z2))) -> c(MARK(2nd(from(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(from(from(y0))), z2))) -> c(MARK(2nd(from(from(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons(y0, y1))), z2))) -> c(MARK(2nd(from(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(from(s(y0))), z2))) -> c(MARK(2nd(from(s(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons1(y0, y1))), z2))) -> c(MARK(2nd(from(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, 2nd(y1))), z2))) -> c(MARK(2nd(cons1(y0, 2nd(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, from(y1))), z2))) -> c(MARK(2nd(cons1(y0, from(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons(y1, y2))))) A__2ND(cons1(z0, cons(2nd(cons1(2nd(y0), y1)), z2))) -> c(MARK(2nd(cons1(2nd(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(from(y0), y1)), z2))) -> c(MARK(2nd(cons1(from(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(s(y0), y1)), z2))) -> c(MARK(2nd(cons1(s(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons1(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, y1)), z2))) -> c(MARK(2nd(cons1(y0, y1)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, s(y1))), z2))) -> c(MARK(2nd(cons1(y0, s(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons1(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons1(y1, y2))))) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(from(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(x0)) A__2ND(cons(x0, cons(s(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(x0)) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(cons(2nd(z0), x2))) A__2ND(cons(x0, cons(from(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(cons(from(z0), x2))) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(cons(cons(z0, z1), x2))) A__2ND(cons(x0, cons(s(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(cons(s(z0), x2))) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(cons(cons1(z0, z1), x2))) A__2ND(cons(x0, cons(x1, x2))) -> c2(MARK(cons(x1, x2))) A__FROM(from(y0)) -> c4(MARK(from(y0))) A__FROM(cons(y0, y1)) -> c4(MARK(cons(y0, y1))) A__FROM(s(y0)) -> c4(MARK(s(y0))) A__FROM(cons1(y0, y1)) -> c4(MARK(cons1(y0, y1))) A__FROM(2nd(cons(y0, y1))) -> c4(MARK(2nd(cons(y0, y1)))) A__FROM(2nd(s(y0))) -> c4(MARK(2nd(s(y0)))) A__FROM(2nd(2nd(2nd(y0)))) -> c4(MARK(2nd(2nd(2nd(y0))))) A__FROM(2nd(2nd(from(y0)))) -> c4(MARK(2nd(2nd(from(y0))))) A__FROM(2nd(2nd(cons(y0, y1)))) -> c4(MARK(2nd(2nd(cons(y0, y1))))) A__FROM(2nd(2nd(s(y0)))) -> c4(MARK(2nd(2nd(s(y0))))) A__FROM(2nd(2nd(cons1(y0, y1)))) -> c4(MARK(2nd(2nd(cons1(y0, y1))))) A__FROM(2nd(2nd(y0))) -> c4(MARK(2nd(2nd(y0)))) A__FROM(2nd(from(y0))) -> c4(MARK(2nd(from(y0)))) A__FROM(2nd(from(2nd(y0)))) -> c4(MARK(2nd(from(2nd(y0))))) A__FROM(2nd(from(from(y0)))) -> c4(MARK(2nd(from(from(y0))))) A__FROM(2nd(from(cons(y0, y1)))) -> c4(MARK(2nd(from(cons(y0, y1))))) A__FROM(2nd(from(s(y0)))) -> c4(MARK(2nd(from(s(y0))))) A__FROM(2nd(from(cons1(y0, y1)))) -> c4(MARK(2nd(from(cons1(y0, y1))))) A__FROM(2nd(cons1(y0, 2nd(y1)))) -> c4(MARK(2nd(cons1(y0, 2nd(y1))))) A__FROM(2nd(cons1(y0, from(y1)))) -> c4(MARK(2nd(cons1(y0, from(y1))))) A__FROM(2nd(cons1(y0, cons(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons(y1, y2))))) A__FROM(2nd(cons1(2nd(y0), y1))) -> c4(MARK(2nd(cons1(2nd(y0), y1)))) A__FROM(2nd(cons1(from(y0), y1))) -> c4(MARK(2nd(cons1(from(y0), y1)))) A__FROM(2nd(cons1(cons(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons(y0, y1), y2)))) A__FROM(2nd(cons1(s(y0), y1))) -> c4(MARK(2nd(cons1(s(y0), y1)))) A__FROM(2nd(cons1(cons1(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__FROM(2nd(cons1(y0, y1))) -> c4(MARK(2nd(cons1(y0, y1)))) A__FROM(2nd(cons1(y0, s(y1)))) -> c4(MARK(2nd(cons1(y0, s(y1))))) A__FROM(2nd(cons1(y0, cons1(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(from(2nd(z0))) -> c7(A__FROM(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(from(from(z0))) -> c7(A__FROM(a__from(mark(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons1(z0, z1))) -> c7(A__FROM(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) S tuples: MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) MARK(2nd(cons1(x0, 2nd(z0)))) -> c6(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(cons1(x0, 2nd(z0)))) MARK(2nd(cons1(x0, from(z0)))) -> c6(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(cons1(x0, from(z0)))) MARK(2nd(cons1(x0, cons(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons1(x0, cons(z0, z1)))) MARK(2nd(cons1(2nd(z0), x1))) -> c6(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(cons1(2nd(z0), x1))) MARK(2nd(cons1(from(z0), x1))) -> c6(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(cons1(from(z0), x1))) MARK(2nd(cons1(cons(z0, z1), x1))) -> c6(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons1(cons(z0, z1), x1))) MARK(2nd(cons1(s(z0), x1))) -> c6(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(cons1(s(z0), x1))) MARK(2nd(cons1(cons1(z0, z1), x1))) -> c6(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(cons1(z0, z1), x1))) MARK(2nd(cons1(x0, x1))) -> c6(MARK(cons1(x0, x1))) MARK(2nd(cons1(x0, s(z0)))) -> c6(MARK(cons1(x0, s(z0)))) MARK(2nd(cons1(x0, cons1(z0, z1)))) -> c6(MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons1(z0, cons(from(y0), z2))) -> c(MARK(from(y0))) A__2ND(cons1(z0, cons(cons(y0, y1), z2))) -> c(MARK(cons(y0, y1))) A__2ND(cons1(z0, cons(s(y0), z2))) -> c(MARK(s(y0))) A__2ND(cons1(z0, cons(cons1(y0, y1), z2))) -> c(MARK(cons1(y0, y1))) A__2ND(cons1(z0, cons(2nd(cons(y0, y1)), z2))) -> c(MARK(2nd(cons(y0, y1)))) A__2ND(cons1(z0, cons(2nd(s(y0)), z2))) -> c(MARK(2nd(s(y0)))) A__2ND(cons1(z0, cons(2nd(2nd(2nd(y0))), z2))) -> c(MARK(2nd(2nd(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(from(y0))), z2))) -> c(MARK(2nd(2nd(from(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(s(y0))), z2))) -> c(MARK(2nd(2nd(s(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons1(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(y0)), z2))) -> c(MARK(2nd(2nd(y0)))) A__2ND(cons1(z0, cons(2nd(from(y0)), z2))) -> c(MARK(2nd(from(y0)))) A__2ND(cons1(z0, cons(2nd(from(2nd(y0))), z2))) -> c(MARK(2nd(from(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(from(from(y0))), z2))) -> c(MARK(2nd(from(from(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons(y0, y1))), z2))) -> c(MARK(2nd(from(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(from(s(y0))), z2))) -> c(MARK(2nd(from(s(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons1(y0, y1))), z2))) -> c(MARK(2nd(from(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, 2nd(y1))), z2))) -> c(MARK(2nd(cons1(y0, 2nd(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, from(y1))), z2))) -> c(MARK(2nd(cons1(y0, from(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons(y1, y2))))) A__2ND(cons1(z0, cons(2nd(cons1(2nd(y0), y1)), z2))) -> c(MARK(2nd(cons1(2nd(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(from(y0), y1)), z2))) -> c(MARK(2nd(cons1(from(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(s(y0), y1)), z2))) -> c(MARK(2nd(cons1(s(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons1(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, y1)), z2))) -> c(MARK(2nd(cons1(y0, y1)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, s(y1))), z2))) -> c(MARK(2nd(cons1(y0, s(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons1(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons1(y1, y2))))) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(from(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(x0)) A__2ND(cons(x0, cons(s(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(x0)) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(cons(2nd(z0), x2))) A__2ND(cons(x0, cons(from(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(cons(from(z0), x2))) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(cons(cons(z0, z1), x2))) A__2ND(cons(x0, cons(s(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(cons(s(z0), x2))) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(cons(cons1(z0, z1), x2))) A__2ND(cons(x0, cons(x1, x2))) -> c2(MARK(cons(x1, x2))) A__FROM(from(y0)) -> c4(MARK(from(y0))) A__FROM(cons(y0, y1)) -> c4(MARK(cons(y0, y1))) A__FROM(s(y0)) -> c4(MARK(s(y0))) A__FROM(cons1(y0, y1)) -> c4(MARK(cons1(y0, y1))) A__FROM(2nd(cons(y0, y1))) -> c4(MARK(2nd(cons(y0, y1)))) A__FROM(2nd(s(y0))) -> c4(MARK(2nd(s(y0)))) A__FROM(2nd(2nd(2nd(y0)))) -> c4(MARK(2nd(2nd(2nd(y0))))) A__FROM(2nd(2nd(from(y0)))) -> c4(MARK(2nd(2nd(from(y0))))) A__FROM(2nd(2nd(cons(y0, y1)))) -> c4(MARK(2nd(2nd(cons(y0, y1))))) A__FROM(2nd(2nd(s(y0)))) -> c4(MARK(2nd(2nd(s(y0))))) A__FROM(2nd(2nd(cons1(y0, y1)))) -> c4(MARK(2nd(2nd(cons1(y0, y1))))) A__FROM(2nd(2nd(y0))) -> c4(MARK(2nd(2nd(y0)))) A__FROM(2nd(from(y0))) -> c4(MARK(2nd(from(y0)))) A__FROM(2nd(from(2nd(y0)))) -> c4(MARK(2nd(from(2nd(y0))))) A__FROM(2nd(from(from(y0)))) -> c4(MARK(2nd(from(from(y0))))) A__FROM(2nd(from(cons(y0, y1)))) -> c4(MARK(2nd(from(cons(y0, y1))))) A__FROM(2nd(from(s(y0)))) -> c4(MARK(2nd(from(s(y0))))) A__FROM(2nd(from(cons1(y0, y1)))) -> c4(MARK(2nd(from(cons1(y0, y1))))) A__FROM(2nd(cons1(y0, 2nd(y1)))) -> c4(MARK(2nd(cons1(y0, 2nd(y1))))) A__FROM(2nd(cons1(y0, from(y1)))) -> c4(MARK(2nd(cons1(y0, from(y1))))) A__FROM(2nd(cons1(y0, cons(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons(y1, y2))))) A__FROM(2nd(cons1(2nd(y0), y1))) -> c4(MARK(2nd(cons1(2nd(y0), y1)))) A__FROM(2nd(cons1(from(y0), y1))) -> c4(MARK(2nd(cons1(from(y0), y1)))) A__FROM(2nd(cons1(cons(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons(y0, y1), y2)))) A__FROM(2nd(cons1(s(y0), y1))) -> c4(MARK(2nd(cons1(s(y0), y1)))) A__FROM(2nd(cons1(cons1(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__FROM(2nd(cons1(y0, y1))) -> c4(MARK(2nd(cons1(y0, y1)))) A__FROM(2nd(cons1(y0, s(y1)))) -> c4(MARK(2nd(cons1(y0, s(y1))))) A__FROM(2nd(cons1(y0, cons1(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(from(2nd(z0))) -> c7(A__FROM(a__2nd(mark(z0))), MARK(2nd(z0))) MARK(from(from(z0))) -> c7(A__FROM(a__from(mark(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons1(z0, z1))) -> c7(A__FROM(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: MARK_1, A__2ND_1, A__FROM_1 Compound Symbols: c8_1, c9_1, c10_1, c11_1, c1_1, c2_1, c6_2, c6_1, c1_2, c2_2, c_1, c4_1, c7_2 ---------------------------------------- (115) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(from(2nd(z0))) -> c7(A__FROM(a__2nd(mark(z0))), MARK(2nd(z0))) by MARK(from(2nd(x0))) -> c7(A__FROM(2nd(mark(x0))), MARK(2nd(x0))) MARK(from(2nd(2nd(z0)))) -> c7(A__FROM(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(from(2nd(from(z0)))) -> c7(A__FROM(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(from(2nd(cons(z0, z1)))) -> c7(A__FROM(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(from(2nd(s(z0)))) -> c7(A__FROM(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(from(2nd(cons1(z0, z1)))) -> c7(A__FROM(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) MARK(2nd(cons1(x0, 2nd(z0)))) -> c6(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(cons1(x0, 2nd(z0)))) MARK(2nd(cons1(x0, from(z0)))) -> c6(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(cons1(x0, from(z0)))) MARK(2nd(cons1(x0, cons(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons1(x0, cons(z0, z1)))) MARK(2nd(cons1(2nd(z0), x1))) -> c6(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(cons1(2nd(z0), x1))) MARK(2nd(cons1(from(z0), x1))) -> c6(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(cons1(from(z0), x1))) MARK(2nd(cons1(cons(z0, z1), x1))) -> c6(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons1(cons(z0, z1), x1))) MARK(2nd(cons1(s(z0), x1))) -> c6(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(cons1(s(z0), x1))) MARK(2nd(cons1(cons1(z0, z1), x1))) -> c6(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(cons1(z0, z1), x1))) MARK(2nd(cons1(x0, x1))) -> c6(MARK(cons1(x0, x1))) MARK(2nd(cons1(x0, s(z0)))) -> c6(MARK(cons1(x0, s(z0)))) MARK(2nd(cons1(x0, cons1(z0, z1)))) -> c6(MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons1(z0, cons(from(y0), z2))) -> c(MARK(from(y0))) A__2ND(cons1(z0, cons(cons(y0, y1), z2))) -> c(MARK(cons(y0, y1))) A__2ND(cons1(z0, cons(s(y0), z2))) -> c(MARK(s(y0))) A__2ND(cons1(z0, cons(cons1(y0, y1), z2))) -> c(MARK(cons1(y0, y1))) A__2ND(cons1(z0, cons(2nd(cons(y0, y1)), z2))) -> c(MARK(2nd(cons(y0, y1)))) A__2ND(cons1(z0, cons(2nd(s(y0)), z2))) -> c(MARK(2nd(s(y0)))) A__2ND(cons1(z0, cons(2nd(2nd(2nd(y0))), z2))) -> c(MARK(2nd(2nd(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(from(y0))), z2))) -> c(MARK(2nd(2nd(from(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(s(y0))), z2))) -> c(MARK(2nd(2nd(s(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons1(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(y0)), z2))) -> c(MARK(2nd(2nd(y0)))) A__2ND(cons1(z0, cons(2nd(from(y0)), z2))) -> c(MARK(2nd(from(y0)))) A__2ND(cons1(z0, cons(2nd(from(2nd(y0))), z2))) -> c(MARK(2nd(from(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(from(from(y0))), z2))) -> c(MARK(2nd(from(from(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons(y0, y1))), z2))) -> c(MARK(2nd(from(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(from(s(y0))), z2))) -> c(MARK(2nd(from(s(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons1(y0, y1))), z2))) -> c(MARK(2nd(from(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, 2nd(y1))), z2))) -> c(MARK(2nd(cons1(y0, 2nd(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, from(y1))), z2))) -> c(MARK(2nd(cons1(y0, from(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons(y1, y2))))) A__2ND(cons1(z0, cons(2nd(cons1(2nd(y0), y1)), z2))) -> c(MARK(2nd(cons1(2nd(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(from(y0), y1)), z2))) -> c(MARK(2nd(cons1(from(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(s(y0), y1)), z2))) -> c(MARK(2nd(cons1(s(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons1(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, y1)), z2))) -> c(MARK(2nd(cons1(y0, y1)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, s(y1))), z2))) -> c(MARK(2nd(cons1(y0, s(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons1(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons1(y1, y2))))) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(from(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(x0)) A__2ND(cons(x0, cons(s(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(x0)) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(cons(2nd(z0), x2))) A__2ND(cons(x0, cons(from(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(cons(from(z0), x2))) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(cons(cons(z0, z1), x2))) A__2ND(cons(x0, cons(s(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(cons(s(z0), x2))) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(cons(cons1(z0, z1), x2))) A__2ND(cons(x0, cons(x1, x2))) -> c2(MARK(cons(x1, x2))) A__FROM(from(y0)) -> c4(MARK(from(y0))) A__FROM(cons(y0, y1)) -> c4(MARK(cons(y0, y1))) A__FROM(s(y0)) -> c4(MARK(s(y0))) A__FROM(cons1(y0, y1)) -> c4(MARK(cons1(y0, y1))) A__FROM(2nd(cons(y0, y1))) -> c4(MARK(2nd(cons(y0, y1)))) A__FROM(2nd(s(y0))) -> c4(MARK(2nd(s(y0)))) A__FROM(2nd(2nd(2nd(y0)))) -> c4(MARK(2nd(2nd(2nd(y0))))) A__FROM(2nd(2nd(from(y0)))) -> c4(MARK(2nd(2nd(from(y0))))) A__FROM(2nd(2nd(cons(y0, y1)))) -> c4(MARK(2nd(2nd(cons(y0, y1))))) A__FROM(2nd(2nd(s(y0)))) -> c4(MARK(2nd(2nd(s(y0))))) A__FROM(2nd(2nd(cons1(y0, y1)))) -> c4(MARK(2nd(2nd(cons1(y0, y1))))) A__FROM(2nd(2nd(y0))) -> c4(MARK(2nd(2nd(y0)))) A__FROM(2nd(from(y0))) -> c4(MARK(2nd(from(y0)))) A__FROM(2nd(from(2nd(y0)))) -> c4(MARK(2nd(from(2nd(y0))))) A__FROM(2nd(from(from(y0)))) -> c4(MARK(2nd(from(from(y0))))) A__FROM(2nd(from(cons(y0, y1)))) -> c4(MARK(2nd(from(cons(y0, y1))))) A__FROM(2nd(from(s(y0)))) -> c4(MARK(2nd(from(s(y0))))) A__FROM(2nd(from(cons1(y0, y1)))) -> c4(MARK(2nd(from(cons1(y0, y1))))) A__FROM(2nd(cons1(y0, 2nd(y1)))) -> c4(MARK(2nd(cons1(y0, 2nd(y1))))) A__FROM(2nd(cons1(y0, from(y1)))) -> c4(MARK(2nd(cons1(y0, from(y1))))) A__FROM(2nd(cons1(y0, cons(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons(y1, y2))))) A__FROM(2nd(cons1(2nd(y0), y1))) -> c4(MARK(2nd(cons1(2nd(y0), y1)))) A__FROM(2nd(cons1(from(y0), y1))) -> c4(MARK(2nd(cons1(from(y0), y1)))) A__FROM(2nd(cons1(cons(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons(y0, y1), y2)))) A__FROM(2nd(cons1(s(y0), y1))) -> c4(MARK(2nd(cons1(s(y0), y1)))) A__FROM(2nd(cons1(cons1(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__FROM(2nd(cons1(y0, y1))) -> c4(MARK(2nd(cons1(y0, y1)))) A__FROM(2nd(cons1(y0, s(y1)))) -> c4(MARK(2nd(cons1(y0, s(y1))))) A__FROM(2nd(cons1(y0, cons1(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(from(from(z0))) -> c7(A__FROM(a__from(mark(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons1(z0, z1))) -> c7(A__FROM(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(from(2nd(x0))) -> c7(A__FROM(2nd(mark(x0))), MARK(2nd(x0))) MARK(from(2nd(2nd(z0)))) -> c7(A__FROM(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(from(2nd(from(z0)))) -> c7(A__FROM(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(from(2nd(cons(z0, z1)))) -> c7(A__FROM(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(from(2nd(s(z0)))) -> c7(A__FROM(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(from(2nd(cons1(z0, z1)))) -> c7(A__FROM(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) S tuples: MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) MARK(2nd(cons1(x0, 2nd(z0)))) -> c6(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(cons1(x0, 2nd(z0)))) MARK(2nd(cons1(x0, from(z0)))) -> c6(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(cons1(x0, from(z0)))) MARK(2nd(cons1(x0, cons(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons1(x0, cons(z0, z1)))) MARK(2nd(cons1(2nd(z0), x1))) -> c6(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(cons1(2nd(z0), x1))) MARK(2nd(cons1(from(z0), x1))) -> c6(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(cons1(from(z0), x1))) MARK(2nd(cons1(cons(z0, z1), x1))) -> c6(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons1(cons(z0, z1), x1))) MARK(2nd(cons1(s(z0), x1))) -> c6(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(cons1(s(z0), x1))) MARK(2nd(cons1(cons1(z0, z1), x1))) -> c6(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(cons1(z0, z1), x1))) MARK(2nd(cons1(x0, x1))) -> c6(MARK(cons1(x0, x1))) MARK(2nd(cons1(x0, s(z0)))) -> c6(MARK(cons1(x0, s(z0)))) MARK(2nd(cons1(x0, cons1(z0, z1)))) -> c6(MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons1(z0, cons(from(y0), z2))) -> c(MARK(from(y0))) A__2ND(cons1(z0, cons(cons(y0, y1), z2))) -> c(MARK(cons(y0, y1))) A__2ND(cons1(z0, cons(s(y0), z2))) -> c(MARK(s(y0))) A__2ND(cons1(z0, cons(cons1(y0, y1), z2))) -> c(MARK(cons1(y0, y1))) A__2ND(cons1(z0, cons(2nd(cons(y0, y1)), z2))) -> c(MARK(2nd(cons(y0, y1)))) A__2ND(cons1(z0, cons(2nd(s(y0)), z2))) -> c(MARK(2nd(s(y0)))) A__2ND(cons1(z0, cons(2nd(2nd(2nd(y0))), z2))) -> c(MARK(2nd(2nd(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(from(y0))), z2))) -> c(MARK(2nd(2nd(from(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(s(y0))), z2))) -> c(MARK(2nd(2nd(s(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons1(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(y0)), z2))) -> c(MARK(2nd(2nd(y0)))) A__2ND(cons1(z0, cons(2nd(from(y0)), z2))) -> c(MARK(2nd(from(y0)))) A__2ND(cons1(z0, cons(2nd(from(2nd(y0))), z2))) -> c(MARK(2nd(from(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(from(from(y0))), z2))) -> c(MARK(2nd(from(from(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons(y0, y1))), z2))) -> c(MARK(2nd(from(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(from(s(y0))), z2))) -> c(MARK(2nd(from(s(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons1(y0, y1))), z2))) -> c(MARK(2nd(from(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, 2nd(y1))), z2))) -> c(MARK(2nd(cons1(y0, 2nd(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, from(y1))), z2))) -> c(MARK(2nd(cons1(y0, from(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons(y1, y2))))) A__2ND(cons1(z0, cons(2nd(cons1(2nd(y0), y1)), z2))) -> c(MARK(2nd(cons1(2nd(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(from(y0), y1)), z2))) -> c(MARK(2nd(cons1(from(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(s(y0), y1)), z2))) -> c(MARK(2nd(cons1(s(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons1(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, y1)), z2))) -> c(MARK(2nd(cons1(y0, y1)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, s(y1))), z2))) -> c(MARK(2nd(cons1(y0, s(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons1(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons1(y1, y2))))) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(from(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(x0)) A__2ND(cons(x0, cons(s(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(x0)) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(cons(2nd(z0), x2))) A__2ND(cons(x0, cons(from(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(cons(from(z0), x2))) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(cons(cons(z0, z1), x2))) A__2ND(cons(x0, cons(s(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(cons(s(z0), x2))) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(cons(cons1(z0, z1), x2))) A__2ND(cons(x0, cons(x1, x2))) -> c2(MARK(cons(x1, x2))) A__FROM(from(y0)) -> c4(MARK(from(y0))) A__FROM(cons(y0, y1)) -> c4(MARK(cons(y0, y1))) A__FROM(s(y0)) -> c4(MARK(s(y0))) A__FROM(cons1(y0, y1)) -> c4(MARK(cons1(y0, y1))) A__FROM(2nd(cons(y0, y1))) -> c4(MARK(2nd(cons(y0, y1)))) A__FROM(2nd(s(y0))) -> c4(MARK(2nd(s(y0)))) A__FROM(2nd(2nd(2nd(y0)))) -> c4(MARK(2nd(2nd(2nd(y0))))) A__FROM(2nd(2nd(from(y0)))) -> c4(MARK(2nd(2nd(from(y0))))) A__FROM(2nd(2nd(cons(y0, y1)))) -> c4(MARK(2nd(2nd(cons(y0, y1))))) A__FROM(2nd(2nd(s(y0)))) -> c4(MARK(2nd(2nd(s(y0))))) A__FROM(2nd(2nd(cons1(y0, y1)))) -> c4(MARK(2nd(2nd(cons1(y0, y1))))) A__FROM(2nd(2nd(y0))) -> c4(MARK(2nd(2nd(y0)))) A__FROM(2nd(from(y0))) -> c4(MARK(2nd(from(y0)))) A__FROM(2nd(from(2nd(y0)))) -> c4(MARK(2nd(from(2nd(y0))))) A__FROM(2nd(from(from(y0)))) -> c4(MARK(2nd(from(from(y0))))) A__FROM(2nd(from(cons(y0, y1)))) -> c4(MARK(2nd(from(cons(y0, y1))))) A__FROM(2nd(from(s(y0)))) -> c4(MARK(2nd(from(s(y0))))) A__FROM(2nd(from(cons1(y0, y1)))) -> c4(MARK(2nd(from(cons1(y0, y1))))) A__FROM(2nd(cons1(y0, 2nd(y1)))) -> c4(MARK(2nd(cons1(y0, 2nd(y1))))) A__FROM(2nd(cons1(y0, from(y1)))) -> c4(MARK(2nd(cons1(y0, from(y1))))) A__FROM(2nd(cons1(y0, cons(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons(y1, y2))))) A__FROM(2nd(cons1(2nd(y0), y1))) -> c4(MARK(2nd(cons1(2nd(y0), y1)))) A__FROM(2nd(cons1(from(y0), y1))) -> c4(MARK(2nd(cons1(from(y0), y1)))) A__FROM(2nd(cons1(cons(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons(y0, y1), y2)))) A__FROM(2nd(cons1(s(y0), y1))) -> c4(MARK(2nd(cons1(s(y0), y1)))) A__FROM(2nd(cons1(cons1(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__FROM(2nd(cons1(y0, y1))) -> c4(MARK(2nd(cons1(y0, y1)))) A__FROM(2nd(cons1(y0, s(y1)))) -> c4(MARK(2nd(cons1(y0, s(y1))))) A__FROM(2nd(cons1(y0, cons1(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(from(from(z0))) -> c7(A__FROM(a__from(mark(z0))), MARK(from(z0))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons1(z0, z1))) -> c7(A__FROM(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(from(2nd(x0))) -> c7(A__FROM(2nd(mark(x0))), MARK(2nd(x0))) MARK(from(2nd(2nd(z0)))) -> c7(A__FROM(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(from(2nd(from(z0)))) -> c7(A__FROM(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(from(2nd(cons(z0, z1)))) -> c7(A__FROM(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(from(2nd(s(z0)))) -> c7(A__FROM(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(from(2nd(cons1(z0, z1)))) -> c7(A__FROM(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: MARK_1, A__2ND_1, A__FROM_1 Compound Symbols: c8_1, c9_1, c10_1, c11_1, c1_1, c2_1, c6_2, c6_1, c1_2, c2_2, c_1, c4_1, c7_2 ---------------------------------------- (117) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(from(from(z0))) -> c7(A__FROM(a__from(mark(z0))), MARK(from(z0))) by MARK(from(from(x0))) -> c7(A__FROM(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(from(from(x0))) -> c7(A__FROM(from(mark(x0))), MARK(from(x0))) MARK(from(from(2nd(z0)))) -> c7(A__FROM(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(from(from(from(z0)))) -> c7(A__FROM(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(from(from(cons(z0, z1)))) -> c7(A__FROM(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(from(from(s(z0)))) -> c7(A__FROM(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(from(from(cons1(z0, z1)))) -> c7(A__FROM(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) MARK(2nd(cons1(x0, 2nd(z0)))) -> c6(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(cons1(x0, 2nd(z0)))) MARK(2nd(cons1(x0, from(z0)))) -> c6(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(cons1(x0, from(z0)))) MARK(2nd(cons1(x0, cons(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons1(x0, cons(z0, z1)))) MARK(2nd(cons1(2nd(z0), x1))) -> c6(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(cons1(2nd(z0), x1))) MARK(2nd(cons1(from(z0), x1))) -> c6(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(cons1(from(z0), x1))) MARK(2nd(cons1(cons(z0, z1), x1))) -> c6(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons1(cons(z0, z1), x1))) MARK(2nd(cons1(s(z0), x1))) -> c6(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(cons1(s(z0), x1))) MARK(2nd(cons1(cons1(z0, z1), x1))) -> c6(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(cons1(z0, z1), x1))) MARK(2nd(cons1(x0, x1))) -> c6(MARK(cons1(x0, x1))) MARK(2nd(cons1(x0, s(z0)))) -> c6(MARK(cons1(x0, s(z0)))) MARK(2nd(cons1(x0, cons1(z0, z1)))) -> c6(MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons1(z0, cons(from(y0), z2))) -> c(MARK(from(y0))) A__2ND(cons1(z0, cons(cons(y0, y1), z2))) -> c(MARK(cons(y0, y1))) A__2ND(cons1(z0, cons(s(y0), z2))) -> c(MARK(s(y0))) A__2ND(cons1(z0, cons(cons1(y0, y1), z2))) -> c(MARK(cons1(y0, y1))) A__2ND(cons1(z0, cons(2nd(cons(y0, y1)), z2))) -> c(MARK(2nd(cons(y0, y1)))) A__2ND(cons1(z0, cons(2nd(s(y0)), z2))) -> c(MARK(2nd(s(y0)))) A__2ND(cons1(z0, cons(2nd(2nd(2nd(y0))), z2))) -> c(MARK(2nd(2nd(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(from(y0))), z2))) -> c(MARK(2nd(2nd(from(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(s(y0))), z2))) -> c(MARK(2nd(2nd(s(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons1(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(y0)), z2))) -> c(MARK(2nd(2nd(y0)))) A__2ND(cons1(z0, cons(2nd(from(y0)), z2))) -> c(MARK(2nd(from(y0)))) A__2ND(cons1(z0, cons(2nd(from(2nd(y0))), z2))) -> c(MARK(2nd(from(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(from(from(y0))), z2))) -> c(MARK(2nd(from(from(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons(y0, y1))), z2))) -> c(MARK(2nd(from(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(from(s(y0))), z2))) -> c(MARK(2nd(from(s(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons1(y0, y1))), z2))) -> c(MARK(2nd(from(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, 2nd(y1))), z2))) -> c(MARK(2nd(cons1(y0, 2nd(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, from(y1))), z2))) -> c(MARK(2nd(cons1(y0, from(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons(y1, y2))))) A__2ND(cons1(z0, cons(2nd(cons1(2nd(y0), y1)), z2))) -> c(MARK(2nd(cons1(2nd(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(from(y0), y1)), z2))) -> c(MARK(2nd(cons1(from(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(s(y0), y1)), z2))) -> c(MARK(2nd(cons1(s(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons1(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, y1)), z2))) -> c(MARK(2nd(cons1(y0, y1)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, s(y1))), z2))) -> c(MARK(2nd(cons1(y0, s(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons1(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons1(y1, y2))))) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(from(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(x0)) A__2ND(cons(x0, cons(s(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(x0)) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(cons(2nd(z0), x2))) A__2ND(cons(x0, cons(from(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(cons(from(z0), x2))) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(cons(cons(z0, z1), x2))) A__2ND(cons(x0, cons(s(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(cons(s(z0), x2))) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(cons(cons1(z0, z1), x2))) A__2ND(cons(x0, cons(x1, x2))) -> c2(MARK(cons(x1, x2))) A__FROM(from(y0)) -> c4(MARK(from(y0))) A__FROM(cons(y0, y1)) -> c4(MARK(cons(y0, y1))) A__FROM(s(y0)) -> c4(MARK(s(y0))) A__FROM(cons1(y0, y1)) -> c4(MARK(cons1(y0, y1))) A__FROM(2nd(cons(y0, y1))) -> c4(MARK(2nd(cons(y0, y1)))) A__FROM(2nd(s(y0))) -> c4(MARK(2nd(s(y0)))) A__FROM(2nd(2nd(2nd(y0)))) -> c4(MARK(2nd(2nd(2nd(y0))))) A__FROM(2nd(2nd(from(y0)))) -> c4(MARK(2nd(2nd(from(y0))))) A__FROM(2nd(2nd(cons(y0, y1)))) -> c4(MARK(2nd(2nd(cons(y0, y1))))) A__FROM(2nd(2nd(s(y0)))) -> c4(MARK(2nd(2nd(s(y0))))) A__FROM(2nd(2nd(cons1(y0, y1)))) -> c4(MARK(2nd(2nd(cons1(y0, y1))))) A__FROM(2nd(2nd(y0))) -> c4(MARK(2nd(2nd(y0)))) A__FROM(2nd(from(y0))) -> c4(MARK(2nd(from(y0)))) A__FROM(2nd(from(2nd(y0)))) -> c4(MARK(2nd(from(2nd(y0))))) A__FROM(2nd(from(from(y0)))) -> c4(MARK(2nd(from(from(y0))))) A__FROM(2nd(from(cons(y0, y1)))) -> c4(MARK(2nd(from(cons(y0, y1))))) A__FROM(2nd(from(s(y0)))) -> c4(MARK(2nd(from(s(y0))))) A__FROM(2nd(from(cons1(y0, y1)))) -> c4(MARK(2nd(from(cons1(y0, y1))))) A__FROM(2nd(cons1(y0, 2nd(y1)))) -> c4(MARK(2nd(cons1(y0, 2nd(y1))))) A__FROM(2nd(cons1(y0, from(y1)))) -> c4(MARK(2nd(cons1(y0, from(y1))))) A__FROM(2nd(cons1(y0, cons(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons(y1, y2))))) A__FROM(2nd(cons1(2nd(y0), y1))) -> c4(MARK(2nd(cons1(2nd(y0), y1)))) A__FROM(2nd(cons1(from(y0), y1))) -> c4(MARK(2nd(cons1(from(y0), y1)))) A__FROM(2nd(cons1(cons(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons(y0, y1), y2)))) A__FROM(2nd(cons1(s(y0), y1))) -> c4(MARK(2nd(cons1(s(y0), y1)))) A__FROM(2nd(cons1(cons1(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__FROM(2nd(cons1(y0, y1))) -> c4(MARK(2nd(cons1(y0, y1)))) A__FROM(2nd(cons1(y0, s(y1)))) -> c4(MARK(2nd(cons1(y0, s(y1))))) A__FROM(2nd(cons1(y0, cons1(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons1(z0, z1))) -> c7(A__FROM(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(from(2nd(x0))) -> c7(A__FROM(2nd(mark(x0))), MARK(2nd(x0))) MARK(from(2nd(2nd(z0)))) -> c7(A__FROM(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(from(2nd(from(z0)))) -> c7(A__FROM(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(from(2nd(cons(z0, z1)))) -> c7(A__FROM(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(from(2nd(s(z0)))) -> c7(A__FROM(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(from(2nd(cons1(z0, z1)))) -> c7(A__FROM(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(from(from(x0))) -> c7(A__FROM(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(from(from(x0))) -> c7(A__FROM(from(mark(x0))), MARK(from(x0))) MARK(from(from(2nd(z0)))) -> c7(A__FROM(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(from(from(from(z0)))) -> c7(A__FROM(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(from(from(cons(z0, z1)))) -> c7(A__FROM(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(from(from(s(z0)))) -> c7(A__FROM(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(from(from(cons1(z0, z1)))) -> c7(A__FROM(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) S tuples: MARK(cons(z0, z1)) -> c8(MARK(z0)) MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) MARK(2nd(cons1(x0, 2nd(z0)))) -> c6(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(cons1(x0, 2nd(z0)))) MARK(2nd(cons1(x0, from(z0)))) -> c6(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(cons1(x0, from(z0)))) MARK(2nd(cons1(x0, cons(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons1(x0, cons(z0, z1)))) MARK(2nd(cons1(2nd(z0), x1))) -> c6(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(cons1(2nd(z0), x1))) MARK(2nd(cons1(from(z0), x1))) -> c6(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(cons1(from(z0), x1))) MARK(2nd(cons1(cons(z0, z1), x1))) -> c6(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons1(cons(z0, z1), x1))) MARK(2nd(cons1(s(z0), x1))) -> c6(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(cons1(s(z0), x1))) MARK(2nd(cons1(cons1(z0, z1), x1))) -> c6(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(cons1(z0, z1), x1))) MARK(2nd(cons1(x0, x1))) -> c6(MARK(cons1(x0, x1))) MARK(2nd(cons1(x0, s(z0)))) -> c6(MARK(cons1(x0, s(z0)))) MARK(2nd(cons1(x0, cons1(z0, z1)))) -> c6(MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons1(z0, cons(from(y0), z2))) -> c(MARK(from(y0))) A__2ND(cons1(z0, cons(cons(y0, y1), z2))) -> c(MARK(cons(y0, y1))) A__2ND(cons1(z0, cons(s(y0), z2))) -> c(MARK(s(y0))) A__2ND(cons1(z0, cons(cons1(y0, y1), z2))) -> c(MARK(cons1(y0, y1))) A__2ND(cons1(z0, cons(2nd(cons(y0, y1)), z2))) -> c(MARK(2nd(cons(y0, y1)))) A__2ND(cons1(z0, cons(2nd(s(y0)), z2))) -> c(MARK(2nd(s(y0)))) A__2ND(cons1(z0, cons(2nd(2nd(2nd(y0))), z2))) -> c(MARK(2nd(2nd(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(from(y0))), z2))) -> c(MARK(2nd(2nd(from(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(s(y0))), z2))) -> c(MARK(2nd(2nd(s(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons1(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(y0)), z2))) -> c(MARK(2nd(2nd(y0)))) A__2ND(cons1(z0, cons(2nd(from(y0)), z2))) -> c(MARK(2nd(from(y0)))) A__2ND(cons1(z0, cons(2nd(from(2nd(y0))), z2))) -> c(MARK(2nd(from(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(from(from(y0))), z2))) -> c(MARK(2nd(from(from(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons(y0, y1))), z2))) -> c(MARK(2nd(from(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(from(s(y0))), z2))) -> c(MARK(2nd(from(s(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons1(y0, y1))), z2))) -> c(MARK(2nd(from(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, 2nd(y1))), z2))) -> c(MARK(2nd(cons1(y0, 2nd(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, from(y1))), z2))) -> c(MARK(2nd(cons1(y0, from(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons(y1, y2))))) A__2ND(cons1(z0, cons(2nd(cons1(2nd(y0), y1)), z2))) -> c(MARK(2nd(cons1(2nd(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(from(y0), y1)), z2))) -> c(MARK(2nd(cons1(from(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(s(y0), y1)), z2))) -> c(MARK(2nd(cons1(s(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons1(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, y1)), z2))) -> c(MARK(2nd(cons1(y0, y1)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, s(y1))), z2))) -> c(MARK(2nd(cons1(y0, s(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons1(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons1(y1, y2))))) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(from(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(x0)) A__2ND(cons(x0, cons(s(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(x0)) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(cons(2nd(z0), x2))) A__2ND(cons(x0, cons(from(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(cons(from(z0), x2))) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(cons(cons(z0, z1), x2))) A__2ND(cons(x0, cons(s(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(cons(s(z0), x2))) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(cons(cons1(z0, z1), x2))) A__2ND(cons(x0, cons(x1, x2))) -> c2(MARK(cons(x1, x2))) A__FROM(from(y0)) -> c4(MARK(from(y0))) A__FROM(cons(y0, y1)) -> c4(MARK(cons(y0, y1))) A__FROM(s(y0)) -> c4(MARK(s(y0))) A__FROM(cons1(y0, y1)) -> c4(MARK(cons1(y0, y1))) A__FROM(2nd(cons(y0, y1))) -> c4(MARK(2nd(cons(y0, y1)))) A__FROM(2nd(s(y0))) -> c4(MARK(2nd(s(y0)))) A__FROM(2nd(2nd(2nd(y0)))) -> c4(MARK(2nd(2nd(2nd(y0))))) A__FROM(2nd(2nd(from(y0)))) -> c4(MARK(2nd(2nd(from(y0))))) A__FROM(2nd(2nd(cons(y0, y1)))) -> c4(MARK(2nd(2nd(cons(y0, y1))))) A__FROM(2nd(2nd(s(y0)))) -> c4(MARK(2nd(2nd(s(y0))))) A__FROM(2nd(2nd(cons1(y0, y1)))) -> c4(MARK(2nd(2nd(cons1(y0, y1))))) A__FROM(2nd(2nd(y0))) -> c4(MARK(2nd(2nd(y0)))) A__FROM(2nd(from(y0))) -> c4(MARK(2nd(from(y0)))) A__FROM(2nd(from(2nd(y0)))) -> c4(MARK(2nd(from(2nd(y0))))) A__FROM(2nd(from(from(y0)))) -> c4(MARK(2nd(from(from(y0))))) A__FROM(2nd(from(cons(y0, y1)))) -> c4(MARK(2nd(from(cons(y0, y1))))) A__FROM(2nd(from(s(y0)))) -> c4(MARK(2nd(from(s(y0))))) A__FROM(2nd(from(cons1(y0, y1)))) -> c4(MARK(2nd(from(cons1(y0, y1))))) A__FROM(2nd(cons1(y0, 2nd(y1)))) -> c4(MARK(2nd(cons1(y0, 2nd(y1))))) A__FROM(2nd(cons1(y0, from(y1)))) -> c4(MARK(2nd(cons1(y0, from(y1))))) A__FROM(2nd(cons1(y0, cons(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons(y1, y2))))) A__FROM(2nd(cons1(2nd(y0), y1))) -> c4(MARK(2nd(cons1(2nd(y0), y1)))) A__FROM(2nd(cons1(from(y0), y1))) -> c4(MARK(2nd(cons1(from(y0), y1)))) A__FROM(2nd(cons1(cons(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons(y0, y1), y2)))) A__FROM(2nd(cons1(s(y0), y1))) -> c4(MARK(2nd(cons1(s(y0), y1)))) A__FROM(2nd(cons1(cons1(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__FROM(2nd(cons1(y0, y1))) -> c4(MARK(2nd(cons1(y0, y1)))) A__FROM(2nd(cons1(y0, s(y1)))) -> c4(MARK(2nd(cons1(y0, s(y1))))) A__FROM(2nd(cons1(y0, cons1(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons1(z0, z1))) -> c7(A__FROM(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(from(2nd(x0))) -> c7(A__FROM(2nd(mark(x0))), MARK(2nd(x0))) MARK(from(2nd(2nd(z0)))) -> c7(A__FROM(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(from(2nd(from(z0)))) -> c7(A__FROM(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(from(2nd(cons(z0, z1)))) -> c7(A__FROM(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(from(2nd(s(z0)))) -> c7(A__FROM(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(from(2nd(cons1(z0, z1)))) -> c7(A__FROM(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(from(from(x0))) -> c7(A__FROM(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(from(from(x0))) -> c7(A__FROM(from(mark(x0))), MARK(from(x0))) MARK(from(from(2nd(z0)))) -> c7(A__FROM(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(from(from(from(z0)))) -> c7(A__FROM(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(from(from(cons(z0, z1)))) -> c7(A__FROM(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(from(from(s(z0)))) -> c7(A__FROM(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(from(from(cons1(z0, z1)))) -> c7(A__FROM(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: MARK_1, A__2ND_1, A__FROM_1 Compound Symbols: c8_1, c9_1, c10_1, c11_1, c1_1, c2_1, c6_2, c6_1, c1_2, c2_2, c_1, c4_1, c7_2 ---------------------------------------- (119) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(cons(z0, z1)) -> c8(MARK(z0)) by MARK(cons(cons(y0, y1), z1)) -> c8(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c8(MARK(s(y0))) MARK(cons(cons1(y0, y1), z1)) -> c8(MARK(cons1(y0, y1))) MARK(cons(2nd(cons(y0, y1)), z1)) -> c8(MARK(2nd(cons(y0, y1)))) MARK(cons(2nd(s(y0)), z1)) -> c8(MARK(2nd(s(y0)))) MARK(cons(2nd(2nd(2nd(y0))), z1)) -> c8(MARK(2nd(2nd(2nd(y0))))) MARK(cons(2nd(2nd(from(y0))), z1)) -> c8(MARK(2nd(2nd(from(y0))))) MARK(cons(2nd(2nd(cons(y0, y1))), z1)) -> c8(MARK(2nd(2nd(cons(y0, y1))))) MARK(cons(2nd(2nd(s(y0))), z1)) -> c8(MARK(2nd(2nd(s(y0))))) MARK(cons(2nd(2nd(cons1(y0, y1))), z1)) -> c8(MARK(2nd(2nd(cons1(y0, y1))))) MARK(cons(2nd(2nd(y0)), z1)) -> c8(MARK(2nd(2nd(y0)))) MARK(cons(2nd(from(y0)), z1)) -> c8(MARK(2nd(from(y0)))) MARK(cons(2nd(from(2nd(y0))), z1)) -> c8(MARK(2nd(from(2nd(y0))))) MARK(cons(2nd(from(from(y0))), z1)) -> c8(MARK(2nd(from(from(y0))))) MARK(cons(2nd(from(cons(y0, y1))), z1)) -> c8(MARK(2nd(from(cons(y0, y1))))) MARK(cons(2nd(from(s(y0))), z1)) -> c8(MARK(2nd(from(s(y0))))) MARK(cons(2nd(from(cons1(y0, y1))), z1)) -> c8(MARK(2nd(from(cons1(y0, y1))))) MARK(cons(2nd(cons1(y0, 2nd(y1))), z1)) -> c8(MARK(2nd(cons1(y0, 2nd(y1))))) MARK(cons(2nd(cons1(y0, from(y1))), z1)) -> c8(MARK(2nd(cons1(y0, from(y1))))) MARK(cons(2nd(cons1(y0, cons(y1, y2))), z1)) -> c8(MARK(2nd(cons1(y0, cons(y1, y2))))) MARK(cons(2nd(cons1(2nd(y0), y1)), z1)) -> c8(MARK(2nd(cons1(2nd(y0), y1)))) MARK(cons(2nd(cons1(from(y0), y1)), z1)) -> c8(MARK(2nd(cons1(from(y0), y1)))) MARK(cons(2nd(cons1(cons(y0, y1), y2)), z1)) -> c8(MARK(2nd(cons1(cons(y0, y1), y2)))) MARK(cons(2nd(cons1(s(y0), y1)), z1)) -> c8(MARK(2nd(cons1(s(y0), y1)))) MARK(cons(2nd(cons1(cons1(y0, y1), y2)), z1)) -> c8(MARK(2nd(cons1(cons1(y0, y1), y2)))) MARK(cons(2nd(cons1(y0, y1)), z1)) -> c8(MARK(2nd(cons1(y0, y1)))) MARK(cons(2nd(cons1(y0, s(y1))), z1)) -> c8(MARK(2nd(cons1(y0, s(y1))))) MARK(cons(2nd(cons1(y0, cons1(y1, y2))), z1)) -> c8(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(cons(from(cons(y0, y1)), z1)) -> c8(MARK(from(cons(y0, y1)))) MARK(cons(from(s(y0)), z1)) -> c8(MARK(from(s(y0)))) MARK(cons(from(cons1(y0, y1)), z1)) -> c8(MARK(from(cons1(y0, y1)))) MARK(cons(from(2nd(y0)), z1)) -> c8(MARK(from(2nd(y0)))) MARK(cons(from(2nd(2nd(y0))), z1)) -> c8(MARK(from(2nd(2nd(y0))))) MARK(cons(from(2nd(from(y0))), z1)) -> c8(MARK(from(2nd(from(y0))))) MARK(cons(from(2nd(cons(y0, y1))), z1)) -> c8(MARK(from(2nd(cons(y0, y1))))) MARK(cons(from(2nd(s(y0))), z1)) -> c8(MARK(from(2nd(s(y0))))) MARK(cons(from(2nd(cons1(y0, y1))), z1)) -> c8(MARK(from(2nd(cons1(y0, y1))))) MARK(cons(from(from(y0)), z1)) -> c8(MARK(from(from(y0)))) MARK(cons(from(from(2nd(y0))), z1)) -> c8(MARK(from(from(2nd(y0))))) MARK(cons(from(from(from(y0))), z1)) -> c8(MARK(from(from(from(y0))))) MARK(cons(from(from(cons(y0, y1))), z1)) -> c8(MARK(from(from(cons(y0, y1))))) MARK(cons(from(from(s(y0))), z1)) -> c8(MARK(from(from(s(y0))))) MARK(cons(from(from(cons1(y0, y1))), z1)) -> c8(MARK(from(from(cons1(y0, y1))))) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) MARK(2nd(cons1(x0, 2nd(z0)))) -> c6(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(cons1(x0, 2nd(z0)))) MARK(2nd(cons1(x0, from(z0)))) -> c6(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(cons1(x0, from(z0)))) MARK(2nd(cons1(x0, cons(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons1(x0, cons(z0, z1)))) MARK(2nd(cons1(2nd(z0), x1))) -> c6(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(cons1(2nd(z0), x1))) MARK(2nd(cons1(from(z0), x1))) -> c6(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(cons1(from(z0), x1))) MARK(2nd(cons1(cons(z0, z1), x1))) -> c6(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons1(cons(z0, z1), x1))) MARK(2nd(cons1(s(z0), x1))) -> c6(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(cons1(s(z0), x1))) MARK(2nd(cons1(cons1(z0, z1), x1))) -> c6(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(cons1(z0, z1), x1))) MARK(2nd(cons1(x0, x1))) -> c6(MARK(cons1(x0, x1))) MARK(2nd(cons1(x0, s(z0)))) -> c6(MARK(cons1(x0, s(z0)))) MARK(2nd(cons1(x0, cons1(z0, z1)))) -> c6(MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons1(z0, cons(from(y0), z2))) -> c(MARK(from(y0))) A__2ND(cons1(z0, cons(cons(y0, y1), z2))) -> c(MARK(cons(y0, y1))) A__2ND(cons1(z0, cons(s(y0), z2))) -> c(MARK(s(y0))) A__2ND(cons1(z0, cons(cons1(y0, y1), z2))) -> c(MARK(cons1(y0, y1))) A__2ND(cons1(z0, cons(2nd(cons(y0, y1)), z2))) -> c(MARK(2nd(cons(y0, y1)))) A__2ND(cons1(z0, cons(2nd(s(y0)), z2))) -> c(MARK(2nd(s(y0)))) A__2ND(cons1(z0, cons(2nd(2nd(2nd(y0))), z2))) -> c(MARK(2nd(2nd(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(from(y0))), z2))) -> c(MARK(2nd(2nd(from(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(s(y0))), z2))) -> c(MARK(2nd(2nd(s(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons1(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(y0)), z2))) -> c(MARK(2nd(2nd(y0)))) A__2ND(cons1(z0, cons(2nd(from(y0)), z2))) -> c(MARK(2nd(from(y0)))) A__2ND(cons1(z0, cons(2nd(from(2nd(y0))), z2))) -> c(MARK(2nd(from(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(from(from(y0))), z2))) -> c(MARK(2nd(from(from(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons(y0, y1))), z2))) -> c(MARK(2nd(from(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(from(s(y0))), z2))) -> c(MARK(2nd(from(s(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons1(y0, y1))), z2))) -> c(MARK(2nd(from(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, 2nd(y1))), z2))) -> c(MARK(2nd(cons1(y0, 2nd(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, from(y1))), z2))) -> c(MARK(2nd(cons1(y0, from(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons(y1, y2))))) A__2ND(cons1(z0, cons(2nd(cons1(2nd(y0), y1)), z2))) -> c(MARK(2nd(cons1(2nd(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(from(y0), y1)), z2))) -> c(MARK(2nd(cons1(from(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(s(y0), y1)), z2))) -> c(MARK(2nd(cons1(s(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons1(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, y1)), z2))) -> c(MARK(2nd(cons1(y0, y1)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, s(y1))), z2))) -> c(MARK(2nd(cons1(y0, s(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons1(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons1(y1, y2))))) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(from(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(x0)) A__2ND(cons(x0, cons(s(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(x0)) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(cons(2nd(z0), x2))) A__2ND(cons(x0, cons(from(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(cons(from(z0), x2))) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(cons(cons(z0, z1), x2))) A__2ND(cons(x0, cons(s(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(cons(s(z0), x2))) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(cons(cons1(z0, z1), x2))) A__2ND(cons(x0, cons(x1, x2))) -> c2(MARK(cons(x1, x2))) A__FROM(from(y0)) -> c4(MARK(from(y0))) A__FROM(cons(y0, y1)) -> c4(MARK(cons(y0, y1))) A__FROM(s(y0)) -> c4(MARK(s(y0))) A__FROM(cons1(y0, y1)) -> c4(MARK(cons1(y0, y1))) A__FROM(2nd(cons(y0, y1))) -> c4(MARK(2nd(cons(y0, y1)))) A__FROM(2nd(s(y0))) -> c4(MARK(2nd(s(y0)))) A__FROM(2nd(2nd(2nd(y0)))) -> c4(MARK(2nd(2nd(2nd(y0))))) A__FROM(2nd(2nd(from(y0)))) -> c4(MARK(2nd(2nd(from(y0))))) A__FROM(2nd(2nd(cons(y0, y1)))) -> c4(MARK(2nd(2nd(cons(y0, y1))))) A__FROM(2nd(2nd(s(y0)))) -> c4(MARK(2nd(2nd(s(y0))))) A__FROM(2nd(2nd(cons1(y0, y1)))) -> c4(MARK(2nd(2nd(cons1(y0, y1))))) A__FROM(2nd(2nd(y0))) -> c4(MARK(2nd(2nd(y0)))) A__FROM(2nd(from(y0))) -> c4(MARK(2nd(from(y0)))) A__FROM(2nd(from(2nd(y0)))) -> c4(MARK(2nd(from(2nd(y0))))) A__FROM(2nd(from(from(y0)))) -> c4(MARK(2nd(from(from(y0))))) A__FROM(2nd(from(cons(y0, y1)))) -> c4(MARK(2nd(from(cons(y0, y1))))) A__FROM(2nd(from(s(y0)))) -> c4(MARK(2nd(from(s(y0))))) A__FROM(2nd(from(cons1(y0, y1)))) -> c4(MARK(2nd(from(cons1(y0, y1))))) A__FROM(2nd(cons1(y0, 2nd(y1)))) -> c4(MARK(2nd(cons1(y0, 2nd(y1))))) A__FROM(2nd(cons1(y0, from(y1)))) -> c4(MARK(2nd(cons1(y0, from(y1))))) A__FROM(2nd(cons1(y0, cons(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons(y1, y2))))) A__FROM(2nd(cons1(2nd(y0), y1))) -> c4(MARK(2nd(cons1(2nd(y0), y1)))) A__FROM(2nd(cons1(from(y0), y1))) -> c4(MARK(2nd(cons1(from(y0), y1)))) A__FROM(2nd(cons1(cons(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons(y0, y1), y2)))) A__FROM(2nd(cons1(s(y0), y1))) -> c4(MARK(2nd(cons1(s(y0), y1)))) A__FROM(2nd(cons1(cons1(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__FROM(2nd(cons1(y0, y1))) -> c4(MARK(2nd(cons1(y0, y1)))) A__FROM(2nd(cons1(y0, s(y1)))) -> c4(MARK(2nd(cons1(y0, s(y1))))) A__FROM(2nd(cons1(y0, cons1(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons1(z0, z1))) -> c7(A__FROM(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(from(2nd(x0))) -> c7(A__FROM(2nd(mark(x0))), MARK(2nd(x0))) MARK(from(2nd(2nd(z0)))) -> c7(A__FROM(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(from(2nd(from(z0)))) -> c7(A__FROM(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(from(2nd(cons(z0, z1)))) -> c7(A__FROM(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(from(2nd(s(z0)))) -> c7(A__FROM(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(from(2nd(cons1(z0, z1)))) -> c7(A__FROM(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(from(from(x0))) -> c7(A__FROM(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(from(from(x0))) -> c7(A__FROM(from(mark(x0))), MARK(from(x0))) MARK(from(from(2nd(z0)))) -> c7(A__FROM(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(from(from(from(z0)))) -> c7(A__FROM(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(from(from(cons(z0, z1)))) -> c7(A__FROM(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(from(from(s(z0)))) -> c7(A__FROM(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(from(from(cons1(z0, z1)))) -> c7(A__FROM(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(cons(cons(y0, y1), z1)) -> c8(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c8(MARK(s(y0))) MARK(cons(cons1(y0, y1), z1)) -> c8(MARK(cons1(y0, y1))) MARK(cons(2nd(cons(y0, y1)), z1)) -> c8(MARK(2nd(cons(y0, y1)))) MARK(cons(2nd(s(y0)), z1)) -> c8(MARK(2nd(s(y0)))) MARK(cons(2nd(2nd(2nd(y0))), z1)) -> c8(MARK(2nd(2nd(2nd(y0))))) MARK(cons(2nd(2nd(from(y0))), z1)) -> c8(MARK(2nd(2nd(from(y0))))) MARK(cons(2nd(2nd(cons(y0, y1))), z1)) -> c8(MARK(2nd(2nd(cons(y0, y1))))) MARK(cons(2nd(2nd(s(y0))), z1)) -> c8(MARK(2nd(2nd(s(y0))))) MARK(cons(2nd(2nd(cons1(y0, y1))), z1)) -> c8(MARK(2nd(2nd(cons1(y0, y1))))) MARK(cons(2nd(2nd(y0)), z1)) -> c8(MARK(2nd(2nd(y0)))) MARK(cons(2nd(from(y0)), z1)) -> c8(MARK(2nd(from(y0)))) MARK(cons(2nd(from(2nd(y0))), z1)) -> c8(MARK(2nd(from(2nd(y0))))) MARK(cons(2nd(from(from(y0))), z1)) -> c8(MARK(2nd(from(from(y0))))) MARK(cons(2nd(from(cons(y0, y1))), z1)) -> c8(MARK(2nd(from(cons(y0, y1))))) MARK(cons(2nd(from(s(y0))), z1)) -> c8(MARK(2nd(from(s(y0))))) MARK(cons(2nd(from(cons1(y0, y1))), z1)) -> c8(MARK(2nd(from(cons1(y0, y1))))) MARK(cons(2nd(cons1(y0, 2nd(y1))), z1)) -> c8(MARK(2nd(cons1(y0, 2nd(y1))))) MARK(cons(2nd(cons1(y0, from(y1))), z1)) -> c8(MARK(2nd(cons1(y0, from(y1))))) MARK(cons(2nd(cons1(y0, cons(y1, y2))), z1)) -> c8(MARK(2nd(cons1(y0, cons(y1, y2))))) MARK(cons(2nd(cons1(2nd(y0), y1)), z1)) -> c8(MARK(2nd(cons1(2nd(y0), y1)))) MARK(cons(2nd(cons1(from(y0), y1)), z1)) -> c8(MARK(2nd(cons1(from(y0), y1)))) MARK(cons(2nd(cons1(cons(y0, y1), y2)), z1)) -> c8(MARK(2nd(cons1(cons(y0, y1), y2)))) MARK(cons(2nd(cons1(s(y0), y1)), z1)) -> c8(MARK(2nd(cons1(s(y0), y1)))) MARK(cons(2nd(cons1(cons1(y0, y1), y2)), z1)) -> c8(MARK(2nd(cons1(cons1(y0, y1), y2)))) MARK(cons(2nd(cons1(y0, y1)), z1)) -> c8(MARK(2nd(cons1(y0, y1)))) MARK(cons(2nd(cons1(y0, s(y1))), z1)) -> c8(MARK(2nd(cons1(y0, s(y1))))) MARK(cons(2nd(cons1(y0, cons1(y1, y2))), z1)) -> c8(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(cons(from(cons(y0, y1)), z1)) -> c8(MARK(from(cons(y0, y1)))) MARK(cons(from(s(y0)), z1)) -> c8(MARK(from(s(y0)))) MARK(cons(from(cons1(y0, y1)), z1)) -> c8(MARK(from(cons1(y0, y1)))) MARK(cons(from(2nd(y0)), z1)) -> c8(MARK(from(2nd(y0)))) MARK(cons(from(2nd(2nd(y0))), z1)) -> c8(MARK(from(2nd(2nd(y0))))) MARK(cons(from(2nd(from(y0))), z1)) -> c8(MARK(from(2nd(from(y0))))) MARK(cons(from(2nd(cons(y0, y1))), z1)) -> c8(MARK(from(2nd(cons(y0, y1))))) MARK(cons(from(2nd(s(y0))), z1)) -> c8(MARK(from(2nd(s(y0))))) MARK(cons(from(2nd(cons1(y0, y1))), z1)) -> c8(MARK(from(2nd(cons1(y0, y1))))) MARK(cons(from(from(y0)), z1)) -> c8(MARK(from(from(y0)))) MARK(cons(from(from(2nd(y0))), z1)) -> c8(MARK(from(from(2nd(y0))))) MARK(cons(from(from(from(y0))), z1)) -> c8(MARK(from(from(from(y0))))) MARK(cons(from(from(cons(y0, y1))), z1)) -> c8(MARK(from(from(cons(y0, y1))))) MARK(cons(from(from(s(y0))), z1)) -> c8(MARK(from(from(s(y0))))) MARK(cons(from(from(cons1(y0, y1))), z1)) -> c8(MARK(from(from(cons1(y0, y1))))) S tuples: MARK(s(z0)) -> c9(MARK(z0)) MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) MARK(2nd(cons1(x0, 2nd(z0)))) -> c6(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(cons1(x0, 2nd(z0)))) MARK(2nd(cons1(x0, from(z0)))) -> c6(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(cons1(x0, from(z0)))) MARK(2nd(cons1(x0, cons(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons1(x0, cons(z0, z1)))) MARK(2nd(cons1(2nd(z0), x1))) -> c6(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(cons1(2nd(z0), x1))) MARK(2nd(cons1(from(z0), x1))) -> c6(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(cons1(from(z0), x1))) MARK(2nd(cons1(cons(z0, z1), x1))) -> c6(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons1(cons(z0, z1), x1))) MARK(2nd(cons1(s(z0), x1))) -> c6(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(cons1(s(z0), x1))) MARK(2nd(cons1(cons1(z0, z1), x1))) -> c6(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(cons1(z0, z1), x1))) MARK(2nd(cons1(x0, x1))) -> c6(MARK(cons1(x0, x1))) MARK(2nd(cons1(x0, s(z0)))) -> c6(MARK(cons1(x0, s(z0)))) MARK(2nd(cons1(x0, cons1(z0, z1)))) -> c6(MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons1(z0, cons(from(y0), z2))) -> c(MARK(from(y0))) A__2ND(cons1(z0, cons(cons(y0, y1), z2))) -> c(MARK(cons(y0, y1))) A__2ND(cons1(z0, cons(s(y0), z2))) -> c(MARK(s(y0))) A__2ND(cons1(z0, cons(cons1(y0, y1), z2))) -> c(MARK(cons1(y0, y1))) A__2ND(cons1(z0, cons(2nd(cons(y0, y1)), z2))) -> c(MARK(2nd(cons(y0, y1)))) A__2ND(cons1(z0, cons(2nd(s(y0)), z2))) -> c(MARK(2nd(s(y0)))) A__2ND(cons1(z0, cons(2nd(2nd(2nd(y0))), z2))) -> c(MARK(2nd(2nd(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(from(y0))), z2))) -> c(MARK(2nd(2nd(from(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(s(y0))), z2))) -> c(MARK(2nd(2nd(s(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons1(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(y0)), z2))) -> c(MARK(2nd(2nd(y0)))) A__2ND(cons1(z0, cons(2nd(from(y0)), z2))) -> c(MARK(2nd(from(y0)))) A__2ND(cons1(z0, cons(2nd(from(2nd(y0))), z2))) -> c(MARK(2nd(from(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(from(from(y0))), z2))) -> c(MARK(2nd(from(from(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons(y0, y1))), z2))) -> c(MARK(2nd(from(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(from(s(y0))), z2))) -> c(MARK(2nd(from(s(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons1(y0, y1))), z2))) -> c(MARK(2nd(from(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, 2nd(y1))), z2))) -> c(MARK(2nd(cons1(y0, 2nd(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, from(y1))), z2))) -> c(MARK(2nd(cons1(y0, from(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons(y1, y2))))) A__2ND(cons1(z0, cons(2nd(cons1(2nd(y0), y1)), z2))) -> c(MARK(2nd(cons1(2nd(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(from(y0), y1)), z2))) -> c(MARK(2nd(cons1(from(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(s(y0), y1)), z2))) -> c(MARK(2nd(cons1(s(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons1(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, y1)), z2))) -> c(MARK(2nd(cons1(y0, y1)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, s(y1))), z2))) -> c(MARK(2nd(cons1(y0, s(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons1(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons1(y1, y2))))) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(from(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(x0)) A__2ND(cons(x0, cons(s(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(x0)) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(cons(2nd(z0), x2))) A__2ND(cons(x0, cons(from(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(cons(from(z0), x2))) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(cons(cons(z0, z1), x2))) A__2ND(cons(x0, cons(s(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(cons(s(z0), x2))) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(cons(cons1(z0, z1), x2))) A__2ND(cons(x0, cons(x1, x2))) -> c2(MARK(cons(x1, x2))) A__FROM(from(y0)) -> c4(MARK(from(y0))) A__FROM(cons(y0, y1)) -> c4(MARK(cons(y0, y1))) A__FROM(s(y0)) -> c4(MARK(s(y0))) A__FROM(cons1(y0, y1)) -> c4(MARK(cons1(y0, y1))) A__FROM(2nd(cons(y0, y1))) -> c4(MARK(2nd(cons(y0, y1)))) A__FROM(2nd(s(y0))) -> c4(MARK(2nd(s(y0)))) A__FROM(2nd(2nd(2nd(y0)))) -> c4(MARK(2nd(2nd(2nd(y0))))) A__FROM(2nd(2nd(from(y0)))) -> c4(MARK(2nd(2nd(from(y0))))) A__FROM(2nd(2nd(cons(y0, y1)))) -> c4(MARK(2nd(2nd(cons(y0, y1))))) A__FROM(2nd(2nd(s(y0)))) -> c4(MARK(2nd(2nd(s(y0))))) A__FROM(2nd(2nd(cons1(y0, y1)))) -> c4(MARK(2nd(2nd(cons1(y0, y1))))) A__FROM(2nd(2nd(y0))) -> c4(MARK(2nd(2nd(y0)))) A__FROM(2nd(from(y0))) -> c4(MARK(2nd(from(y0)))) A__FROM(2nd(from(2nd(y0)))) -> c4(MARK(2nd(from(2nd(y0))))) A__FROM(2nd(from(from(y0)))) -> c4(MARK(2nd(from(from(y0))))) A__FROM(2nd(from(cons(y0, y1)))) -> c4(MARK(2nd(from(cons(y0, y1))))) A__FROM(2nd(from(s(y0)))) -> c4(MARK(2nd(from(s(y0))))) A__FROM(2nd(from(cons1(y0, y1)))) -> c4(MARK(2nd(from(cons1(y0, y1))))) A__FROM(2nd(cons1(y0, 2nd(y1)))) -> c4(MARK(2nd(cons1(y0, 2nd(y1))))) A__FROM(2nd(cons1(y0, from(y1)))) -> c4(MARK(2nd(cons1(y0, from(y1))))) A__FROM(2nd(cons1(y0, cons(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons(y1, y2))))) A__FROM(2nd(cons1(2nd(y0), y1))) -> c4(MARK(2nd(cons1(2nd(y0), y1)))) A__FROM(2nd(cons1(from(y0), y1))) -> c4(MARK(2nd(cons1(from(y0), y1)))) A__FROM(2nd(cons1(cons(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons(y0, y1), y2)))) A__FROM(2nd(cons1(s(y0), y1))) -> c4(MARK(2nd(cons1(s(y0), y1)))) A__FROM(2nd(cons1(cons1(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__FROM(2nd(cons1(y0, y1))) -> c4(MARK(2nd(cons1(y0, y1)))) A__FROM(2nd(cons1(y0, s(y1)))) -> c4(MARK(2nd(cons1(y0, s(y1))))) A__FROM(2nd(cons1(y0, cons1(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons1(z0, z1))) -> c7(A__FROM(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(from(2nd(x0))) -> c7(A__FROM(2nd(mark(x0))), MARK(2nd(x0))) MARK(from(2nd(2nd(z0)))) -> c7(A__FROM(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(from(2nd(from(z0)))) -> c7(A__FROM(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(from(2nd(cons(z0, z1)))) -> c7(A__FROM(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(from(2nd(s(z0)))) -> c7(A__FROM(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(from(2nd(cons1(z0, z1)))) -> c7(A__FROM(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(from(from(x0))) -> c7(A__FROM(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(from(from(x0))) -> c7(A__FROM(from(mark(x0))), MARK(from(x0))) MARK(from(from(2nd(z0)))) -> c7(A__FROM(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(from(from(from(z0)))) -> c7(A__FROM(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(from(from(cons(z0, z1)))) -> c7(A__FROM(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(from(from(s(z0)))) -> c7(A__FROM(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(from(from(cons1(z0, z1)))) -> c7(A__FROM(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(cons(cons(y0, y1), z1)) -> c8(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c8(MARK(s(y0))) MARK(cons(cons1(y0, y1), z1)) -> c8(MARK(cons1(y0, y1))) MARK(cons(2nd(cons(y0, y1)), z1)) -> c8(MARK(2nd(cons(y0, y1)))) MARK(cons(2nd(s(y0)), z1)) -> c8(MARK(2nd(s(y0)))) MARK(cons(2nd(2nd(2nd(y0))), z1)) -> c8(MARK(2nd(2nd(2nd(y0))))) MARK(cons(2nd(2nd(from(y0))), z1)) -> c8(MARK(2nd(2nd(from(y0))))) MARK(cons(2nd(2nd(cons(y0, y1))), z1)) -> c8(MARK(2nd(2nd(cons(y0, y1))))) MARK(cons(2nd(2nd(s(y0))), z1)) -> c8(MARK(2nd(2nd(s(y0))))) MARK(cons(2nd(2nd(cons1(y0, y1))), z1)) -> c8(MARK(2nd(2nd(cons1(y0, y1))))) MARK(cons(2nd(2nd(y0)), z1)) -> c8(MARK(2nd(2nd(y0)))) MARK(cons(2nd(from(y0)), z1)) -> c8(MARK(2nd(from(y0)))) MARK(cons(2nd(from(2nd(y0))), z1)) -> c8(MARK(2nd(from(2nd(y0))))) MARK(cons(2nd(from(from(y0))), z1)) -> c8(MARK(2nd(from(from(y0))))) MARK(cons(2nd(from(cons(y0, y1))), z1)) -> c8(MARK(2nd(from(cons(y0, y1))))) MARK(cons(2nd(from(s(y0))), z1)) -> c8(MARK(2nd(from(s(y0))))) MARK(cons(2nd(from(cons1(y0, y1))), z1)) -> c8(MARK(2nd(from(cons1(y0, y1))))) MARK(cons(2nd(cons1(y0, 2nd(y1))), z1)) -> c8(MARK(2nd(cons1(y0, 2nd(y1))))) MARK(cons(2nd(cons1(y0, from(y1))), z1)) -> c8(MARK(2nd(cons1(y0, from(y1))))) MARK(cons(2nd(cons1(y0, cons(y1, y2))), z1)) -> c8(MARK(2nd(cons1(y0, cons(y1, y2))))) MARK(cons(2nd(cons1(2nd(y0), y1)), z1)) -> c8(MARK(2nd(cons1(2nd(y0), y1)))) MARK(cons(2nd(cons1(from(y0), y1)), z1)) -> c8(MARK(2nd(cons1(from(y0), y1)))) MARK(cons(2nd(cons1(cons(y0, y1), y2)), z1)) -> c8(MARK(2nd(cons1(cons(y0, y1), y2)))) MARK(cons(2nd(cons1(s(y0), y1)), z1)) -> c8(MARK(2nd(cons1(s(y0), y1)))) MARK(cons(2nd(cons1(cons1(y0, y1), y2)), z1)) -> c8(MARK(2nd(cons1(cons1(y0, y1), y2)))) MARK(cons(2nd(cons1(y0, y1)), z1)) -> c8(MARK(2nd(cons1(y0, y1)))) MARK(cons(2nd(cons1(y0, s(y1))), z1)) -> c8(MARK(2nd(cons1(y0, s(y1))))) MARK(cons(2nd(cons1(y0, cons1(y1, y2))), z1)) -> c8(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(cons(from(cons(y0, y1)), z1)) -> c8(MARK(from(cons(y0, y1)))) MARK(cons(from(s(y0)), z1)) -> c8(MARK(from(s(y0)))) MARK(cons(from(cons1(y0, y1)), z1)) -> c8(MARK(from(cons1(y0, y1)))) MARK(cons(from(2nd(y0)), z1)) -> c8(MARK(from(2nd(y0)))) MARK(cons(from(2nd(2nd(y0))), z1)) -> c8(MARK(from(2nd(2nd(y0))))) MARK(cons(from(2nd(from(y0))), z1)) -> c8(MARK(from(2nd(from(y0))))) MARK(cons(from(2nd(cons(y0, y1))), z1)) -> c8(MARK(from(2nd(cons(y0, y1))))) MARK(cons(from(2nd(s(y0))), z1)) -> c8(MARK(from(2nd(s(y0))))) MARK(cons(from(2nd(cons1(y0, y1))), z1)) -> c8(MARK(from(2nd(cons1(y0, y1))))) MARK(cons(from(from(y0)), z1)) -> c8(MARK(from(from(y0)))) MARK(cons(from(from(2nd(y0))), z1)) -> c8(MARK(from(from(2nd(y0))))) MARK(cons(from(from(from(y0))), z1)) -> c8(MARK(from(from(from(y0))))) MARK(cons(from(from(cons(y0, y1))), z1)) -> c8(MARK(from(from(cons(y0, y1))))) MARK(cons(from(from(s(y0))), z1)) -> c8(MARK(from(from(s(y0))))) MARK(cons(from(from(cons1(y0, y1))), z1)) -> c8(MARK(from(from(cons1(y0, y1))))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: MARK_1, A__2ND_1, A__FROM_1 Compound Symbols: c9_1, c10_1, c11_1, c1_1, c2_1, c6_2, c6_1, c1_2, c2_2, c_1, c4_1, c7_2, c8_1 ---------------------------------------- (121) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(s(z0)) -> c9(MARK(z0)) by MARK(s(s(y0))) -> c9(MARK(s(y0))) MARK(s(cons1(y0, y1))) -> c9(MARK(cons1(y0, y1))) MARK(s(2nd(cons(y0, y1)))) -> c9(MARK(2nd(cons(y0, y1)))) MARK(s(2nd(s(y0)))) -> c9(MARK(2nd(s(y0)))) MARK(s(2nd(2nd(2nd(y0))))) -> c9(MARK(2nd(2nd(2nd(y0))))) MARK(s(2nd(2nd(from(y0))))) -> c9(MARK(2nd(2nd(from(y0))))) MARK(s(2nd(2nd(cons(y0, y1))))) -> c9(MARK(2nd(2nd(cons(y0, y1))))) MARK(s(2nd(2nd(s(y0))))) -> c9(MARK(2nd(2nd(s(y0))))) MARK(s(2nd(2nd(cons1(y0, y1))))) -> c9(MARK(2nd(2nd(cons1(y0, y1))))) MARK(s(2nd(2nd(y0)))) -> c9(MARK(2nd(2nd(y0)))) MARK(s(2nd(from(y0)))) -> c9(MARK(2nd(from(y0)))) MARK(s(2nd(from(2nd(y0))))) -> c9(MARK(2nd(from(2nd(y0))))) MARK(s(2nd(from(from(y0))))) -> c9(MARK(2nd(from(from(y0))))) MARK(s(2nd(from(cons(y0, y1))))) -> c9(MARK(2nd(from(cons(y0, y1))))) MARK(s(2nd(from(s(y0))))) -> c9(MARK(2nd(from(s(y0))))) MARK(s(2nd(from(cons1(y0, y1))))) -> c9(MARK(2nd(from(cons1(y0, y1))))) MARK(s(2nd(cons1(y0, 2nd(y1))))) -> c9(MARK(2nd(cons1(y0, 2nd(y1))))) MARK(s(2nd(cons1(y0, from(y1))))) -> c9(MARK(2nd(cons1(y0, from(y1))))) MARK(s(2nd(cons1(y0, cons(y1, y2))))) -> c9(MARK(2nd(cons1(y0, cons(y1, y2))))) MARK(s(2nd(cons1(2nd(y0), y1)))) -> c9(MARK(2nd(cons1(2nd(y0), y1)))) MARK(s(2nd(cons1(from(y0), y1)))) -> c9(MARK(2nd(cons1(from(y0), y1)))) MARK(s(2nd(cons1(cons(y0, y1), y2)))) -> c9(MARK(2nd(cons1(cons(y0, y1), y2)))) MARK(s(2nd(cons1(s(y0), y1)))) -> c9(MARK(2nd(cons1(s(y0), y1)))) MARK(s(2nd(cons1(cons1(y0, y1), y2)))) -> c9(MARK(2nd(cons1(cons1(y0, y1), y2)))) MARK(s(2nd(cons1(y0, y1)))) -> c9(MARK(2nd(cons1(y0, y1)))) MARK(s(2nd(cons1(y0, s(y1))))) -> c9(MARK(2nd(cons1(y0, s(y1))))) MARK(s(2nd(cons1(y0, cons1(y1, y2))))) -> c9(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(s(from(cons(y0, y1)))) -> c9(MARK(from(cons(y0, y1)))) MARK(s(from(s(y0)))) -> c9(MARK(from(s(y0)))) MARK(s(from(cons1(y0, y1)))) -> c9(MARK(from(cons1(y0, y1)))) MARK(s(from(2nd(y0)))) -> c9(MARK(from(2nd(y0)))) MARK(s(from(2nd(2nd(y0))))) -> c9(MARK(from(2nd(2nd(y0))))) MARK(s(from(2nd(from(y0))))) -> c9(MARK(from(2nd(from(y0))))) MARK(s(from(2nd(cons(y0, y1))))) -> c9(MARK(from(2nd(cons(y0, y1))))) MARK(s(from(2nd(s(y0))))) -> c9(MARK(from(2nd(s(y0))))) MARK(s(from(2nd(cons1(y0, y1))))) -> c9(MARK(from(2nd(cons1(y0, y1))))) MARK(s(from(from(y0)))) -> c9(MARK(from(from(y0)))) MARK(s(from(from(2nd(y0))))) -> c9(MARK(from(from(2nd(y0))))) MARK(s(from(from(from(y0))))) -> c9(MARK(from(from(from(y0))))) MARK(s(from(from(cons(y0, y1))))) -> c9(MARK(from(from(cons(y0, y1))))) MARK(s(from(from(s(y0))))) -> c9(MARK(from(from(s(y0))))) MARK(s(from(from(cons1(y0, y1))))) -> c9(MARK(from(from(cons1(y0, y1))))) MARK(s(cons(cons(y0, y1), y2))) -> c9(MARK(cons(cons(y0, y1), y2))) MARK(s(cons(s(y0), y1))) -> c9(MARK(cons(s(y0), y1))) MARK(s(cons(cons1(y0, y1), y2))) -> c9(MARK(cons(cons1(y0, y1), y2))) MARK(s(cons(2nd(cons(y0, y1)), y2))) -> c9(MARK(cons(2nd(cons(y0, y1)), y2))) MARK(s(cons(2nd(s(y0)), y1))) -> c9(MARK(cons(2nd(s(y0)), y1))) MARK(s(cons(2nd(2nd(2nd(y0))), y1))) -> c9(MARK(cons(2nd(2nd(2nd(y0))), y1))) MARK(s(cons(2nd(2nd(from(y0))), y1))) -> c9(MARK(cons(2nd(2nd(from(y0))), y1))) MARK(s(cons(2nd(2nd(cons(y0, y1))), y2))) -> c9(MARK(cons(2nd(2nd(cons(y0, y1))), y2))) MARK(s(cons(2nd(2nd(s(y0))), y1))) -> c9(MARK(cons(2nd(2nd(s(y0))), y1))) MARK(s(cons(2nd(2nd(cons1(y0, y1))), y2))) -> c9(MARK(cons(2nd(2nd(cons1(y0, y1))), y2))) MARK(s(cons(2nd(2nd(y0)), y1))) -> c9(MARK(cons(2nd(2nd(y0)), y1))) MARK(s(cons(2nd(from(y0)), y1))) -> c9(MARK(cons(2nd(from(y0)), y1))) MARK(s(cons(2nd(from(2nd(y0))), y1))) -> c9(MARK(cons(2nd(from(2nd(y0))), y1))) MARK(s(cons(2nd(from(from(y0))), y1))) -> c9(MARK(cons(2nd(from(from(y0))), y1))) MARK(s(cons(2nd(from(cons(y0, y1))), y2))) -> c9(MARK(cons(2nd(from(cons(y0, y1))), y2))) MARK(s(cons(2nd(from(s(y0))), y1))) -> c9(MARK(cons(2nd(from(s(y0))), y1))) MARK(s(cons(2nd(from(cons1(y0, y1))), y2))) -> c9(MARK(cons(2nd(from(cons1(y0, y1))), y2))) MARK(s(cons(2nd(cons1(y0, 2nd(y1))), y2))) -> c9(MARK(cons(2nd(cons1(y0, 2nd(y1))), y2))) MARK(s(cons(2nd(cons1(y0, from(y1))), y2))) -> c9(MARK(cons(2nd(cons1(y0, from(y1))), y2))) MARK(s(cons(2nd(cons1(y0, cons(y1, y2))), y3))) -> c9(MARK(cons(2nd(cons1(y0, cons(y1, y2))), y3))) MARK(s(cons(2nd(cons1(2nd(y0), y1)), y2))) -> c9(MARK(cons(2nd(cons1(2nd(y0), y1)), y2))) MARK(s(cons(2nd(cons1(from(y0), y1)), y2))) -> c9(MARK(cons(2nd(cons1(from(y0), y1)), y2))) MARK(s(cons(2nd(cons1(cons(y0, y1), y2)), y3))) -> c9(MARK(cons(2nd(cons1(cons(y0, y1), y2)), y3))) MARK(s(cons(2nd(cons1(s(y0), y1)), y2))) -> c9(MARK(cons(2nd(cons1(s(y0), y1)), y2))) MARK(s(cons(2nd(cons1(cons1(y0, y1), y2)), y3))) -> c9(MARK(cons(2nd(cons1(cons1(y0, y1), y2)), y3))) MARK(s(cons(2nd(cons1(y0, y1)), y2))) -> c9(MARK(cons(2nd(cons1(y0, y1)), y2))) MARK(s(cons(2nd(cons1(y0, s(y1))), y2))) -> c9(MARK(cons(2nd(cons1(y0, s(y1))), y2))) MARK(s(cons(2nd(cons1(y0, cons1(y1, y2))), y3))) -> c9(MARK(cons(2nd(cons1(y0, cons1(y1, y2))), y3))) MARK(s(cons(from(cons(y0, y1)), y2))) -> c9(MARK(cons(from(cons(y0, y1)), y2))) MARK(s(cons(from(s(y0)), y1))) -> c9(MARK(cons(from(s(y0)), y1))) MARK(s(cons(from(cons1(y0, y1)), y2))) -> c9(MARK(cons(from(cons1(y0, y1)), y2))) MARK(s(cons(from(2nd(y0)), y1))) -> c9(MARK(cons(from(2nd(y0)), y1))) MARK(s(cons(from(2nd(2nd(y0))), y1))) -> c9(MARK(cons(from(2nd(2nd(y0))), y1))) MARK(s(cons(from(2nd(from(y0))), y1))) -> c9(MARK(cons(from(2nd(from(y0))), y1))) MARK(s(cons(from(2nd(cons(y0, y1))), y2))) -> c9(MARK(cons(from(2nd(cons(y0, y1))), y2))) MARK(s(cons(from(2nd(s(y0))), y1))) -> c9(MARK(cons(from(2nd(s(y0))), y1))) MARK(s(cons(from(2nd(cons1(y0, y1))), y2))) -> c9(MARK(cons(from(2nd(cons1(y0, y1))), y2))) MARK(s(cons(from(from(y0)), y1))) -> c9(MARK(cons(from(from(y0)), y1))) MARK(s(cons(from(from(2nd(y0))), y1))) -> c9(MARK(cons(from(from(2nd(y0))), y1))) MARK(s(cons(from(from(from(y0))), y1))) -> c9(MARK(cons(from(from(from(y0))), y1))) MARK(s(cons(from(from(cons(y0, y1))), y2))) -> c9(MARK(cons(from(from(cons(y0, y1))), y2))) MARK(s(cons(from(from(s(y0))), y1))) -> c9(MARK(cons(from(from(s(y0))), y1))) MARK(s(cons(from(from(cons1(y0, y1))), y2))) -> c9(MARK(cons(from(from(cons1(y0, y1))), y2))) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) MARK(2nd(cons1(x0, 2nd(z0)))) -> c6(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(cons1(x0, 2nd(z0)))) MARK(2nd(cons1(x0, from(z0)))) -> c6(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(cons1(x0, from(z0)))) MARK(2nd(cons1(x0, cons(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons1(x0, cons(z0, z1)))) MARK(2nd(cons1(2nd(z0), x1))) -> c6(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(cons1(2nd(z0), x1))) MARK(2nd(cons1(from(z0), x1))) -> c6(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(cons1(from(z0), x1))) MARK(2nd(cons1(cons(z0, z1), x1))) -> c6(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons1(cons(z0, z1), x1))) MARK(2nd(cons1(s(z0), x1))) -> c6(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(cons1(s(z0), x1))) MARK(2nd(cons1(cons1(z0, z1), x1))) -> c6(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(cons1(z0, z1), x1))) MARK(2nd(cons1(x0, x1))) -> c6(MARK(cons1(x0, x1))) MARK(2nd(cons1(x0, s(z0)))) -> c6(MARK(cons1(x0, s(z0)))) MARK(2nd(cons1(x0, cons1(z0, z1)))) -> c6(MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons1(z0, cons(from(y0), z2))) -> c(MARK(from(y0))) A__2ND(cons1(z0, cons(cons(y0, y1), z2))) -> c(MARK(cons(y0, y1))) A__2ND(cons1(z0, cons(s(y0), z2))) -> c(MARK(s(y0))) A__2ND(cons1(z0, cons(cons1(y0, y1), z2))) -> c(MARK(cons1(y0, y1))) A__2ND(cons1(z0, cons(2nd(cons(y0, y1)), z2))) -> c(MARK(2nd(cons(y0, y1)))) A__2ND(cons1(z0, cons(2nd(s(y0)), z2))) -> c(MARK(2nd(s(y0)))) A__2ND(cons1(z0, cons(2nd(2nd(2nd(y0))), z2))) -> c(MARK(2nd(2nd(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(from(y0))), z2))) -> c(MARK(2nd(2nd(from(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(s(y0))), z2))) -> c(MARK(2nd(2nd(s(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons1(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(y0)), z2))) -> c(MARK(2nd(2nd(y0)))) A__2ND(cons1(z0, cons(2nd(from(y0)), z2))) -> c(MARK(2nd(from(y0)))) A__2ND(cons1(z0, cons(2nd(from(2nd(y0))), z2))) -> c(MARK(2nd(from(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(from(from(y0))), z2))) -> c(MARK(2nd(from(from(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons(y0, y1))), z2))) -> c(MARK(2nd(from(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(from(s(y0))), z2))) -> c(MARK(2nd(from(s(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons1(y0, y1))), z2))) -> c(MARK(2nd(from(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, 2nd(y1))), z2))) -> c(MARK(2nd(cons1(y0, 2nd(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, from(y1))), z2))) -> c(MARK(2nd(cons1(y0, from(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons(y1, y2))))) A__2ND(cons1(z0, cons(2nd(cons1(2nd(y0), y1)), z2))) -> c(MARK(2nd(cons1(2nd(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(from(y0), y1)), z2))) -> c(MARK(2nd(cons1(from(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(s(y0), y1)), z2))) -> c(MARK(2nd(cons1(s(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons1(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, y1)), z2))) -> c(MARK(2nd(cons1(y0, y1)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, s(y1))), z2))) -> c(MARK(2nd(cons1(y0, s(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons1(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons1(y1, y2))))) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(from(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(x0)) A__2ND(cons(x0, cons(s(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(x0)) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(cons(2nd(z0), x2))) A__2ND(cons(x0, cons(from(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(cons(from(z0), x2))) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(cons(cons(z0, z1), x2))) A__2ND(cons(x0, cons(s(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(cons(s(z0), x2))) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(cons(cons1(z0, z1), x2))) A__2ND(cons(x0, cons(x1, x2))) -> c2(MARK(cons(x1, x2))) A__FROM(from(y0)) -> c4(MARK(from(y0))) A__FROM(cons(y0, y1)) -> c4(MARK(cons(y0, y1))) A__FROM(s(y0)) -> c4(MARK(s(y0))) A__FROM(cons1(y0, y1)) -> c4(MARK(cons1(y0, y1))) A__FROM(2nd(cons(y0, y1))) -> c4(MARK(2nd(cons(y0, y1)))) A__FROM(2nd(s(y0))) -> c4(MARK(2nd(s(y0)))) A__FROM(2nd(2nd(2nd(y0)))) -> c4(MARK(2nd(2nd(2nd(y0))))) A__FROM(2nd(2nd(from(y0)))) -> c4(MARK(2nd(2nd(from(y0))))) A__FROM(2nd(2nd(cons(y0, y1)))) -> c4(MARK(2nd(2nd(cons(y0, y1))))) A__FROM(2nd(2nd(s(y0)))) -> c4(MARK(2nd(2nd(s(y0))))) A__FROM(2nd(2nd(cons1(y0, y1)))) -> c4(MARK(2nd(2nd(cons1(y0, y1))))) A__FROM(2nd(2nd(y0))) -> c4(MARK(2nd(2nd(y0)))) A__FROM(2nd(from(y0))) -> c4(MARK(2nd(from(y0)))) A__FROM(2nd(from(2nd(y0)))) -> c4(MARK(2nd(from(2nd(y0))))) A__FROM(2nd(from(from(y0)))) -> c4(MARK(2nd(from(from(y0))))) A__FROM(2nd(from(cons(y0, y1)))) -> c4(MARK(2nd(from(cons(y0, y1))))) A__FROM(2nd(from(s(y0)))) -> c4(MARK(2nd(from(s(y0))))) A__FROM(2nd(from(cons1(y0, y1)))) -> c4(MARK(2nd(from(cons1(y0, y1))))) A__FROM(2nd(cons1(y0, 2nd(y1)))) -> c4(MARK(2nd(cons1(y0, 2nd(y1))))) A__FROM(2nd(cons1(y0, from(y1)))) -> c4(MARK(2nd(cons1(y0, from(y1))))) A__FROM(2nd(cons1(y0, cons(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons(y1, y2))))) A__FROM(2nd(cons1(2nd(y0), y1))) -> c4(MARK(2nd(cons1(2nd(y0), y1)))) A__FROM(2nd(cons1(from(y0), y1))) -> c4(MARK(2nd(cons1(from(y0), y1)))) A__FROM(2nd(cons1(cons(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons(y0, y1), y2)))) A__FROM(2nd(cons1(s(y0), y1))) -> c4(MARK(2nd(cons1(s(y0), y1)))) A__FROM(2nd(cons1(cons1(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__FROM(2nd(cons1(y0, y1))) -> c4(MARK(2nd(cons1(y0, y1)))) A__FROM(2nd(cons1(y0, s(y1)))) -> c4(MARK(2nd(cons1(y0, s(y1))))) A__FROM(2nd(cons1(y0, cons1(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons1(z0, z1))) -> c7(A__FROM(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(from(2nd(x0))) -> c7(A__FROM(2nd(mark(x0))), MARK(2nd(x0))) MARK(from(2nd(2nd(z0)))) -> c7(A__FROM(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(from(2nd(from(z0)))) -> c7(A__FROM(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(from(2nd(cons(z0, z1)))) -> c7(A__FROM(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(from(2nd(s(z0)))) -> c7(A__FROM(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(from(2nd(cons1(z0, z1)))) -> c7(A__FROM(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(from(from(x0))) -> c7(A__FROM(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(from(from(x0))) -> c7(A__FROM(from(mark(x0))), MARK(from(x0))) MARK(from(from(2nd(z0)))) -> c7(A__FROM(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(from(from(from(z0)))) -> c7(A__FROM(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(from(from(cons(z0, z1)))) -> c7(A__FROM(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(from(from(s(z0)))) -> c7(A__FROM(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(from(from(cons1(z0, z1)))) -> c7(A__FROM(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(cons(cons(y0, y1), z1)) -> c8(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c8(MARK(s(y0))) MARK(cons(cons1(y0, y1), z1)) -> c8(MARK(cons1(y0, y1))) MARK(cons(2nd(cons(y0, y1)), z1)) -> c8(MARK(2nd(cons(y0, y1)))) MARK(cons(2nd(s(y0)), z1)) -> c8(MARK(2nd(s(y0)))) MARK(cons(2nd(2nd(2nd(y0))), z1)) -> c8(MARK(2nd(2nd(2nd(y0))))) MARK(cons(2nd(2nd(from(y0))), z1)) -> c8(MARK(2nd(2nd(from(y0))))) MARK(cons(2nd(2nd(cons(y0, y1))), z1)) -> c8(MARK(2nd(2nd(cons(y0, y1))))) MARK(cons(2nd(2nd(s(y0))), z1)) -> c8(MARK(2nd(2nd(s(y0))))) MARK(cons(2nd(2nd(cons1(y0, y1))), z1)) -> c8(MARK(2nd(2nd(cons1(y0, y1))))) MARK(cons(2nd(2nd(y0)), z1)) -> c8(MARK(2nd(2nd(y0)))) MARK(cons(2nd(from(y0)), z1)) -> c8(MARK(2nd(from(y0)))) MARK(cons(2nd(from(2nd(y0))), z1)) -> c8(MARK(2nd(from(2nd(y0))))) MARK(cons(2nd(from(from(y0))), z1)) -> c8(MARK(2nd(from(from(y0))))) MARK(cons(2nd(from(cons(y0, y1))), z1)) -> c8(MARK(2nd(from(cons(y0, y1))))) MARK(cons(2nd(from(s(y0))), z1)) -> c8(MARK(2nd(from(s(y0))))) MARK(cons(2nd(from(cons1(y0, y1))), z1)) -> c8(MARK(2nd(from(cons1(y0, y1))))) MARK(cons(2nd(cons1(y0, 2nd(y1))), z1)) -> c8(MARK(2nd(cons1(y0, 2nd(y1))))) MARK(cons(2nd(cons1(y0, from(y1))), z1)) -> c8(MARK(2nd(cons1(y0, from(y1))))) MARK(cons(2nd(cons1(y0, cons(y1, y2))), z1)) -> c8(MARK(2nd(cons1(y0, cons(y1, y2))))) MARK(cons(2nd(cons1(2nd(y0), y1)), z1)) -> c8(MARK(2nd(cons1(2nd(y0), y1)))) MARK(cons(2nd(cons1(from(y0), y1)), z1)) -> c8(MARK(2nd(cons1(from(y0), y1)))) MARK(cons(2nd(cons1(cons(y0, y1), y2)), z1)) -> c8(MARK(2nd(cons1(cons(y0, y1), y2)))) MARK(cons(2nd(cons1(s(y0), y1)), z1)) -> c8(MARK(2nd(cons1(s(y0), y1)))) MARK(cons(2nd(cons1(cons1(y0, y1), y2)), z1)) -> c8(MARK(2nd(cons1(cons1(y0, y1), y2)))) MARK(cons(2nd(cons1(y0, y1)), z1)) -> c8(MARK(2nd(cons1(y0, y1)))) MARK(cons(2nd(cons1(y0, s(y1))), z1)) -> c8(MARK(2nd(cons1(y0, s(y1))))) MARK(cons(2nd(cons1(y0, cons1(y1, y2))), z1)) -> c8(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(cons(from(cons(y0, y1)), z1)) -> c8(MARK(from(cons(y0, y1)))) MARK(cons(from(s(y0)), z1)) -> c8(MARK(from(s(y0)))) MARK(cons(from(cons1(y0, y1)), z1)) -> c8(MARK(from(cons1(y0, y1)))) MARK(cons(from(2nd(y0)), z1)) -> c8(MARK(from(2nd(y0)))) MARK(cons(from(2nd(2nd(y0))), z1)) -> c8(MARK(from(2nd(2nd(y0))))) MARK(cons(from(2nd(from(y0))), z1)) -> c8(MARK(from(2nd(from(y0))))) MARK(cons(from(2nd(cons(y0, y1))), z1)) -> c8(MARK(from(2nd(cons(y0, y1))))) MARK(cons(from(2nd(s(y0))), z1)) -> c8(MARK(from(2nd(s(y0))))) MARK(cons(from(2nd(cons1(y0, y1))), z1)) -> c8(MARK(from(2nd(cons1(y0, y1))))) MARK(cons(from(from(y0)), z1)) -> c8(MARK(from(from(y0)))) MARK(cons(from(from(2nd(y0))), z1)) -> c8(MARK(from(from(2nd(y0))))) MARK(cons(from(from(from(y0))), z1)) -> c8(MARK(from(from(from(y0))))) MARK(cons(from(from(cons(y0, y1))), z1)) -> c8(MARK(from(from(cons(y0, y1))))) MARK(cons(from(from(s(y0))), z1)) -> c8(MARK(from(from(s(y0))))) MARK(cons(from(from(cons1(y0, y1))), z1)) -> c8(MARK(from(from(cons1(y0, y1))))) MARK(s(s(y0))) -> c9(MARK(s(y0))) MARK(s(cons1(y0, y1))) -> c9(MARK(cons1(y0, y1))) MARK(s(2nd(cons(y0, y1)))) -> c9(MARK(2nd(cons(y0, y1)))) MARK(s(2nd(s(y0)))) -> c9(MARK(2nd(s(y0)))) MARK(s(2nd(2nd(2nd(y0))))) -> c9(MARK(2nd(2nd(2nd(y0))))) MARK(s(2nd(2nd(from(y0))))) -> c9(MARK(2nd(2nd(from(y0))))) MARK(s(2nd(2nd(cons(y0, y1))))) -> c9(MARK(2nd(2nd(cons(y0, y1))))) MARK(s(2nd(2nd(s(y0))))) -> c9(MARK(2nd(2nd(s(y0))))) MARK(s(2nd(2nd(cons1(y0, y1))))) -> c9(MARK(2nd(2nd(cons1(y0, y1))))) MARK(s(2nd(2nd(y0)))) -> c9(MARK(2nd(2nd(y0)))) MARK(s(2nd(from(y0)))) -> c9(MARK(2nd(from(y0)))) MARK(s(2nd(from(2nd(y0))))) -> c9(MARK(2nd(from(2nd(y0))))) MARK(s(2nd(from(from(y0))))) -> c9(MARK(2nd(from(from(y0))))) MARK(s(2nd(from(cons(y0, y1))))) -> c9(MARK(2nd(from(cons(y0, y1))))) MARK(s(2nd(from(s(y0))))) -> c9(MARK(2nd(from(s(y0))))) MARK(s(2nd(from(cons1(y0, y1))))) -> c9(MARK(2nd(from(cons1(y0, y1))))) MARK(s(2nd(cons1(y0, 2nd(y1))))) -> c9(MARK(2nd(cons1(y0, 2nd(y1))))) MARK(s(2nd(cons1(y0, from(y1))))) -> c9(MARK(2nd(cons1(y0, from(y1))))) MARK(s(2nd(cons1(y0, cons(y1, y2))))) -> c9(MARK(2nd(cons1(y0, cons(y1, y2))))) MARK(s(2nd(cons1(2nd(y0), y1)))) -> c9(MARK(2nd(cons1(2nd(y0), y1)))) MARK(s(2nd(cons1(from(y0), y1)))) -> c9(MARK(2nd(cons1(from(y0), y1)))) MARK(s(2nd(cons1(cons(y0, y1), y2)))) -> c9(MARK(2nd(cons1(cons(y0, y1), y2)))) MARK(s(2nd(cons1(s(y0), y1)))) -> c9(MARK(2nd(cons1(s(y0), y1)))) MARK(s(2nd(cons1(cons1(y0, y1), y2)))) -> c9(MARK(2nd(cons1(cons1(y0, y1), y2)))) MARK(s(2nd(cons1(y0, y1)))) -> c9(MARK(2nd(cons1(y0, y1)))) MARK(s(2nd(cons1(y0, s(y1))))) -> c9(MARK(2nd(cons1(y0, s(y1))))) MARK(s(2nd(cons1(y0, cons1(y1, y2))))) -> c9(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(s(from(cons(y0, y1)))) -> c9(MARK(from(cons(y0, y1)))) MARK(s(from(s(y0)))) -> c9(MARK(from(s(y0)))) MARK(s(from(cons1(y0, y1)))) -> c9(MARK(from(cons1(y0, y1)))) MARK(s(from(2nd(y0)))) -> c9(MARK(from(2nd(y0)))) MARK(s(from(2nd(2nd(y0))))) -> c9(MARK(from(2nd(2nd(y0))))) MARK(s(from(2nd(from(y0))))) -> c9(MARK(from(2nd(from(y0))))) MARK(s(from(2nd(cons(y0, y1))))) -> c9(MARK(from(2nd(cons(y0, y1))))) MARK(s(from(2nd(s(y0))))) -> c9(MARK(from(2nd(s(y0))))) MARK(s(from(2nd(cons1(y0, y1))))) -> c9(MARK(from(2nd(cons1(y0, y1))))) MARK(s(from(from(y0)))) -> c9(MARK(from(from(y0)))) MARK(s(from(from(2nd(y0))))) -> c9(MARK(from(from(2nd(y0))))) MARK(s(from(from(from(y0))))) -> c9(MARK(from(from(from(y0))))) MARK(s(from(from(cons(y0, y1))))) -> c9(MARK(from(from(cons(y0, y1))))) MARK(s(from(from(s(y0))))) -> c9(MARK(from(from(s(y0))))) MARK(s(from(from(cons1(y0, y1))))) -> c9(MARK(from(from(cons1(y0, y1))))) MARK(s(cons(cons(y0, y1), y2))) -> c9(MARK(cons(cons(y0, y1), y2))) MARK(s(cons(s(y0), y1))) -> c9(MARK(cons(s(y0), y1))) MARK(s(cons(cons1(y0, y1), y2))) -> c9(MARK(cons(cons1(y0, y1), y2))) MARK(s(cons(2nd(cons(y0, y1)), y2))) -> c9(MARK(cons(2nd(cons(y0, y1)), y2))) MARK(s(cons(2nd(s(y0)), y1))) -> c9(MARK(cons(2nd(s(y0)), y1))) MARK(s(cons(2nd(2nd(2nd(y0))), y1))) -> c9(MARK(cons(2nd(2nd(2nd(y0))), y1))) MARK(s(cons(2nd(2nd(from(y0))), y1))) -> c9(MARK(cons(2nd(2nd(from(y0))), y1))) MARK(s(cons(2nd(2nd(cons(y0, y1))), y2))) -> c9(MARK(cons(2nd(2nd(cons(y0, y1))), y2))) MARK(s(cons(2nd(2nd(s(y0))), y1))) -> c9(MARK(cons(2nd(2nd(s(y0))), y1))) MARK(s(cons(2nd(2nd(cons1(y0, y1))), y2))) -> c9(MARK(cons(2nd(2nd(cons1(y0, y1))), y2))) MARK(s(cons(2nd(2nd(y0)), y1))) -> c9(MARK(cons(2nd(2nd(y0)), y1))) MARK(s(cons(2nd(from(y0)), y1))) -> c9(MARK(cons(2nd(from(y0)), y1))) MARK(s(cons(2nd(from(2nd(y0))), y1))) -> c9(MARK(cons(2nd(from(2nd(y0))), y1))) MARK(s(cons(2nd(from(from(y0))), y1))) -> c9(MARK(cons(2nd(from(from(y0))), y1))) MARK(s(cons(2nd(from(cons(y0, y1))), y2))) -> c9(MARK(cons(2nd(from(cons(y0, y1))), y2))) MARK(s(cons(2nd(from(s(y0))), y1))) -> c9(MARK(cons(2nd(from(s(y0))), y1))) MARK(s(cons(2nd(from(cons1(y0, y1))), y2))) -> c9(MARK(cons(2nd(from(cons1(y0, y1))), y2))) MARK(s(cons(2nd(cons1(y0, 2nd(y1))), y2))) -> c9(MARK(cons(2nd(cons1(y0, 2nd(y1))), y2))) MARK(s(cons(2nd(cons1(y0, from(y1))), y2))) -> c9(MARK(cons(2nd(cons1(y0, from(y1))), y2))) MARK(s(cons(2nd(cons1(y0, cons(y1, y2))), y3))) -> c9(MARK(cons(2nd(cons1(y0, cons(y1, y2))), y3))) MARK(s(cons(2nd(cons1(2nd(y0), y1)), y2))) -> c9(MARK(cons(2nd(cons1(2nd(y0), y1)), y2))) MARK(s(cons(2nd(cons1(from(y0), y1)), y2))) -> c9(MARK(cons(2nd(cons1(from(y0), y1)), y2))) MARK(s(cons(2nd(cons1(cons(y0, y1), y2)), y3))) -> c9(MARK(cons(2nd(cons1(cons(y0, y1), y2)), y3))) MARK(s(cons(2nd(cons1(s(y0), y1)), y2))) -> c9(MARK(cons(2nd(cons1(s(y0), y1)), y2))) MARK(s(cons(2nd(cons1(cons1(y0, y1), y2)), y3))) -> c9(MARK(cons(2nd(cons1(cons1(y0, y1), y2)), y3))) MARK(s(cons(2nd(cons1(y0, y1)), y2))) -> c9(MARK(cons(2nd(cons1(y0, y1)), y2))) MARK(s(cons(2nd(cons1(y0, s(y1))), y2))) -> c9(MARK(cons(2nd(cons1(y0, s(y1))), y2))) MARK(s(cons(2nd(cons1(y0, cons1(y1, y2))), y3))) -> c9(MARK(cons(2nd(cons1(y0, cons1(y1, y2))), y3))) MARK(s(cons(from(cons(y0, y1)), y2))) -> c9(MARK(cons(from(cons(y0, y1)), y2))) MARK(s(cons(from(s(y0)), y1))) -> c9(MARK(cons(from(s(y0)), y1))) MARK(s(cons(from(cons1(y0, y1)), y2))) -> c9(MARK(cons(from(cons1(y0, y1)), y2))) MARK(s(cons(from(2nd(y0)), y1))) -> c9(MARK(cons(from(2nd(y0)), y1))) MARK(s(cons(from(2nd(2nd(y0))), y1))) -> c9(MARK(cons(from(2nd(2nd(y0))), y1))) MARK(s(cons(from(2nd(from(y0))), y1))) -> c9(MARK(cons(from(2nd(from(y0))), y1))) MARK(s(cons(from(2nd(cons(y0, y1))), y2))) -> c9(MARK(cons(from(2nd(cons(y0, y1))), y2))) MARK(s(cons(from(2nd(s(y0))), y1))) -> c9(MARK(cons(from(2nd(s(y0))), y1))) MARK(s(cons(from(2nd(cons1(y0, y1))), y2))) -> c9(MARK(cons(from(2nd(cons1(y0, y1))), y2))) MARK(s(cons(from(from(y0)), y1))) -> c9(MARK(cons(from(from(y0)), y1))) MARK(s(cons(from(from(2nd(y0))), y1))) -> c9(MARK(cons(from(from(2nd(y0))), y1))) MARK(s(cons(from(from(from(y0))), y1))) -> c9(MARK(cons(from(from(from(y0))), y1))) MARK(s(cons(from(from(cons(y0, y1))), y2))) -> c9(MARK(cons(from(from(cons(y0, y1))), y2))) MARK(s(cons(from(from(s(y0))), y1))) -> c9(MARK(cons(from(from(s(y0))), y1))) MARK(s(cons(from(from(cons1(y0, y1))), y2))) -> c9(MARK(cons(from(from(cons1(y0, y1))), y2))) S tuples: MARK(cons1(z0, z1)) -> c10(MARK(z0)) MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) MARK(2nd(cons1(x0, 2nd(z0)))) -> c6(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(cons1(x0, 2nd(z0)))) MARK(2nd(cons1(x0, from(z0)))) -> c6(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(cons1(x0, from(z0)))) MARK(2nd(cons1(x0, cons(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons1(x0, cons(z0, z1)))) MARK(2nd(cons1(2nd(z0), x1))) -> c6(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(cons1(2nd(z0), x1))) MARK(2nd(cons1(from(z0), x1))) -> c6(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(cons1(from(z0), x1))) MARK(2nd(cons1(cons(z0, z1), x1))) -> c6(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons1(cons(z0, z1), x1))) MARK(2nd(cons1(s(z0), x1))) -> c6(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(cons1(s(z0), x1))) MARK(2nd(cons1(cons1(z0, z1), x1))) -> c6(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(cons1(z0, z1), x1))) MARK(2nd(cons1(x0, x1))) -> c6(MARK(cons1(x0, x1))) MARK(2nd(cons1(x0, s(z0)))) -> c6(MARK(cons1(x0, s(z0)))) MARK(2nd(cons1(x0, cons1(z0, z1)))) -> c6(MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons1(z0, cons(from(y0), z2))) -> c(MARK(from(y0))) A__2ND(cons1(z0, cons(cons(y0, y1), z2))) -> c(MARK(cons(y0, y1))) A__2ND(cons1(z0, cons(s(y0), z2))) -> c(MARK(s(y0))) A__2ND(cons1(z0, cons(cons1(y0, y1), z2))) -> c(MARK(cons1(y0, y1))) A__2ND(cons1(z0, cons(2nd(cons(y0, y1)), z2))) -> c(MARK(2nd(cons(y0, y1)))) A__2ND(cons1(z0, cons(2nd(s(y0)), z2))) -> c(MARK(2nd(s(y0)))) A__2ND(cons1(z0, cons(2nd(2nd(2nd(y0))), z2))) -> c(MARK(2nd(2nd(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(from(y0))), z2))) -> c(MARK(2nd(2nd(from(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(s(y0))), z2))) -> c(MARK(2nd(2nd(s(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons1(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(y0)), z2))) -> c(MARK(2nd(2nd(y0)))) A__2ND(cons1(z0, cons(2nd(from(y0)), z2))) -> c(MARK(2nd(from(y0)))) A__2ND(cons1(z0, cons(2nd(from(2nd(y0))), z2))) -> c(MARK(2nd(from(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(from(from(y0))), z2))) -> c(MARK(2nd(from(from(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons(y0, y1))), z2))) -> c(MARK(2nd(from(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(from(s(y0))), z2))) -> c(MARK(2nd(from(s(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons1(y0, y1))), z2))) -> c(MARK(2nd(from(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, 2nd(y1))), z2))) -> c(MARK(2nd(cons1(y0, 2nd(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, from(y1))), z2))) -> c(MARK(2nd(cons1(y0, from(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons(y1, y2))))) A__2ND(cons1(z0, cons(2nd(cons1(2nd(y0), y1)), z2))) -> c(MARK(2nd(cons1(2nd(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(from(y0), y1)), z2))) -> c(MARK(2nd(cons1(from(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(s(y0), y1)), z2))) -> c(MARK(2nd(cons1(s(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons1(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, y1)), z2))) -> c(MARK(2nd(cons1(y0, y1)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, s(y1))), z2))) -> c(MARK(2nd(cons1(y0, s(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons1(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons1(y1, y2))))) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(from(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(x0)) A__2ND(cons(x0, cons(s(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(x0)) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(cons(2nd(z0), x2))) A__2ND(cons(x0, cons(from(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(cons(from(z0), x2))) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(cons(cons(z0, z1), x2))) A__2ND(cons(x0, cons(s(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(cons(s(z0), x2))) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(cons(cons1(z0, z1), x2))) A__2ND(cons(x0, cons(x1, x2))) -> c2(MARK(cons(x1, x2))) A__FROM(from(y0)) -> c4(MARK(from(y0))) A__FROM(cons(y0, y1)) -> c4(MARK(cons(y0, y1))) A__FROM(s(y0)) -> c4(MARK(s(y0))) A__FROM(cons1(y0, y1)) -> c4(MARK(cons1(y0, y1))) A__FROM(2nd(cons(y0, y1))) -> c4(MARK(2nd(cons(y0, y1)))) A__FROM(2nd(s(y0))) -> c4(MARK(2nd(s(y0)))) A__FROM(2nd(2nd(2nd(y0)))) -> c4(MARK(2nd(2nd(2nd(y0))))) A__FROM(2nd(2nd(from(y0)))) -> c4(MARK(2nd(2nd(from(y0))))) A__FROM(2nd(2nd(cons(y0, y1)))) -> c4(MARK(2nd(2nd(cons(y0, y1))))) A__FROM(2nd(2nd(s(y0)))) -> c4(MARK(2nd(2nd(s(y0))))) A__FROM(2nd(2nd(cons1(y0, y1)))) -> c4(MARK(2nd(2nd(cons1(y0, y1))))) A__FROM(2nd(2nd(y0))) -> c4(MARK(2nd(2nd(y0)))) A__FROM(2nd(from(y0))) -> c4(MARK(2nd(from(y0)))) A__FROM(2nd(from(2nd(y0)))) -> c4(MARK(2nd(from(2nd(y0))))) A__FROM(2nd(from(from(y0)))) -> c4(MARK(2nd(from(from(y0))))) A__FROM(2nd(from(cons(y0, y1)))) -> c4(MARK(2nd(from(cons(y0, y1))))) A__FROM(2nd(from(s(y0)))) -> c4(MARK(2nd(from(s(y0))))) A__FROM(2nd(from(cons1(y0, y1)))) -> c4(MARK(2nd(from(cons1(y0, y1))))) A__FROM(2nd(cons1(y0, 2nd(y1)))) -> c4(MARK(2nd(cons1(y0, 2nd(y1))))) A__FROM(2nd(cons1(y0, from(y1)))) -> c4(MARK(2nd(cons1(y0, from(y1))))) A__FROM(2nd(cons1(y0, cons(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons(y1, y2))))) A__FROM(2nd(cons1(2nd(y0), y1))) -> c4(MARK(2nd(cons1(2nd(y0), y1)))) A__FROM(2nd(cons1(from(y0), y1))) -> c4(MARK(2nd(cons1(from(y0), y1)))) A__FROM(2nd(cons1(cons(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons(y0, y1), y2)))) A__FROM(2nd(cons1(s(y0), y1))) -> c4(MARK(2nd(cons1(s(y0), y1)))) A__FROM(2nd(cons1(cons1(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__FROM(2nd(cons1(y0, y1))) -> c4(MARK(2nd(cons1(y0, y1)))) A__FROM(2nd(cons1(y0, s(y1)))) -> c4(MARK(2nd(cons1(y0, s(y1))))) A__FROM(2nd(cons1(y0, cons1(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons1(z0, z1))) -> c7(A__FROM(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(from(2nd(x0))) -> c7(A__FROM(2nd(mark(x0))), MARK(2nd(x0))) MARK(from(2nd(2nd(z0)))) -> c7(A__FROM(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(from(2nd(from(z0)))) -> c7(A__FROM(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(from(2nd(cons(z0, z1)))) -> c7(A__FROM(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(from(2nd(s(z0)))) -> c7(A__FROM(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(from(2nd(cons1(z0, z1)))) -> c7(A__FROM(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(from(from(x0))) -> c7(A__FROM(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(from(from(x0))) -> c7(A__FROM(from(mark(x0))), MARK(from(x0))) MARK(from(from(2nd(z0)))) -> c7(A__FROM(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(from(from(from(z0)))) -> c7(A__FROM(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(from(from(cons(z0, z1)))) -> c7(A__FROM(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(from(from(s(z0)))) -> c7(A__FROM(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(from(from(cons1(z0, z1)))) -> c7(A__FROM(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(cons(cons(y0, y1), z1)) -> c8(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c8(MARK(s(y0))) MARK(cons(cons1(y0, y1), z1)) -> c8(MARK(cons1(y0, y1))) MARK(cons(2nd(cons(y0, y1)), z1)) -> c8(MARK(2nd(cons(y0, y1)))) MARK(cons(2nd(s(y0)), z1)) -> c8(MARK(2nd(s(y0)))) MARK(cons(2nd(2nd(2nd(y0))), z1)) -> c8(MARK(2nd(2nd(2nd(y0))))) MARK(cons(2nd(2nd(from(y0))), z1)) -> c8(MARK(2nd(2nd(from(y0))))) MARK(cons(2nd(2nd(cons(y0, y1))), z1)) -> c8(MARK(2nd(2nd(cons(y0, y1))))) MARK(cons(2nd(2nd(s(y0))), z1)) -> c8(MARK(2nd(2nd(s(y0))))) MARK(cons(2nd(2nd(cons1(y0, y1))), z1)) -> c8(MARK(2nd(2nd(cons1(y0, y1))))) MARK(cons(2nd(2nd(y0)), z1)) -> c8(MARK(2nd(2nd(y0)))) MARK(cons(2nd(from(y0)), z1)) -> c8(MARK(2nd(from(y0)))) MARK(cons(2nd(from(2nd(y0))), z1)) -> c8(MARK(2nd(from(2nd(y0))))) MARK(cons(2nd(from(from(y0))), z1)) -> c8(MARK(2nd(from(from(y0))))) MARK(cons(2nd(from(cons(y0, y1))), z1)) -> c8(MARK(2nd(from(cons(y0, y1))))) MARK(cons(2nd(from(s(y0))), z1)) -> c8(MARK(2nd(from(s(y0))))) MARK(cons(2nd(from(cons1(y0, y1))), z1)) -> c8(MARK(2nd(from(cons1(y0, y1))))) MARK(cons(2nd(cons1(y0, 2nd(y1))), z1)) -> c8(MARK(2nd(cons1(y0, 2nd(y1))))) MARK(cons(2nd(cons1(y0, from(y1))), z1)) -> c8(MARK(2nd(cons1(y0, from(y1))))) MARK(cons(2nd(cons1(y0, cons(y1, y2))), z1)) -> c8(MARK(2nd(cons1(y0, cons(y1, y2))))) MARK(cons(2nd(cons1(2nd(y0), y1)), z1)) -> c8(MARK(2nd(cons1(2nd(y0), y1)))) MARK(cons(2nd(cons1(from(y0), y1)), z1)) -> c8(MARK(2nd(cons1(from(y0), y1)))) MARK(cons(2nd(cons1(cons(y0, y1), y2)), z1)) -> c8(MARK(2nd(cons1(cons(y0, y1), y2)))) MARK(cons(2nd(cons1(s(y0), y1)), z1)) -> c8(MARK(2nd(cons1(s(y0), y1)))) MARK(cons(2nd(cons1(cons1(y0, y1), y2)), z1)) -> c8(MARK(2nd(cons1(cons1(y0, y1), y2)))) MARK(cons(2nd(cons1(y0, y1)), z1)) -> c8(MARK(2nd(cons1(y0, y1)))) MARK(cons(2nd(cons1(y0, s(y1))), z1)) -> c8(MARK(2nd(cons1(y0, s(y1))))) MARK(cons(2nd(cons1(y0, cons1(y1, y2))), z1)) -> c8(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(cons(from(cons(y0, y1)), z1)) -> c8(MARK(from(cons(y0, y1)))) MARK(cons(from(s(y0)), z1)) -> c8(MARK(from(s(y0)))) MARK(cons(from(cons1(y0, y1)), z1)) -> c8(MARK(from(cons1(y0, y1)))) MARK(cons(from(2nd(y0)), z1)) -> c8(MARK(from(2nd(y0)))) MARK(cons(from(2nd(2nd(y0))), z1)) -> c8(MARK(from(2nd(2nd(y0))))) MARK(cons(from(2nd(from(y0))), z1)) -> c8(MARK(from(2nd(from(y0))))) MARK(cons(from(2nd(cons(y0, y1))), z1)) -> c8(MARK(from(2nd(cons(y0, y1))))) MARK(cons(from(2nd(s(y0))), z1)) -> c8(MARK(from(2nd(s(y0))))) MARK(cons(from(2nd(cons1(y0, y1))), z1)) -> c8(MARK(from(2nd(cons1(y0, y1))))) MARK(cons(from(from(y0)), z1)) -> c8(MARK(from(from(y0)))) MARK(cons(from(from(2nd(y0))), z1)) -> c8(MARK(from(from(2nd(y0))))) MARK(cons(from(from(from(y0))), z1)) -> c8(MARK(from(from(from(y0))))) MARK(cons(from(from(cons(y0, y1))), z1)) -> c8(MARK(from(from(cons(y0, y1))))) MARK(cons(from(from(s(y0))), z1)) -> c8(MARK(from(from(s(y0))))) MARK(cons(from(from(cons1(y0, y1))), z1)) -> c8(MARK(from(from(cons1(y0, y1))))) MARK(s(s(y0))) -> c9(MARK(s(y0))) MARK(s(cons1(y0, y1))) -> c9(MARK(cons1(y0, y1))) MARK(s(2nd(cons(y0, y1)))) -> c9(MARK(2nd(cons(y0, y1)))) MARK(s(2nd(s(y0)))) -> c9(MARK(2nd(s(y0)))) MARK(s(2nd(2nd(2nd(y0))))) -> c9(MARK(2nd(2nd(2nd(y0))))) MARK(s(2nd(2nd(from(y0))))) -> c9(MARK(2nd(2nd(from(y0))))) MARK(s(2nd(2nd(cons(y0, y1))))) -> c9(MARK(2nd(2nd(cons(y0, y1))))) MARK(s(2nd(2nd(s(y0))))) -> c9(MARK(2nd(2nd(s(y0))))) MARK(s(2nd(2nd(cons1(y0, y1))))) -> c9(MARK(2nd(2nd(cons1(y0, y1))))) MARK(s(2nd(2nd(y0)))) -> c9(MARK(2nd(2nd(y0)))) MARK(s(2nd(from(y0)))) -> c9(MARK(2nd(from(y0)))) MARK(s(2nd(from(2nd(y0))))) -> c9(MARK(2nd(from(2nd(y0))))) MARK(s(2nd(from(from(y0))))) -> c9(MARK(2nd(from(from(y0))))) MARK(s(2nd(from(cons(y0, y1))))) -> c9(MARK(2nd(from(cons(y0, y1))))) MARK(s(2nd(from(s(y0))))) -> c9(MARK(2nd(from(s(y0))))) MARK(s(2nd(from(cons1(y0, y1))))) -> c9(MARK(2nd(from(cons1(y0, y1))))) MARK(s(2nd(cons1(y0, 2nd(y1))))) -> c9(MARK(2nd(cons1(y0, 2nd(y1))))) MARK(s(2nd(cons1(y0, from(y1))))) -> c9(MARK(2nd(cons1(y0, from(y1))))) MARK(s(2nd(cons1(y0, cons(y1, y2))))) -> c9(MARK(2nd(cons1(y0, cons(y1, y2))))) MARK(s(2nd(cons1(2nd(y0), y1)))) -> c9(MARK(2nd(cons1(2nd(y0), y1)))) MARK(s(2nd(cons1(from(y0), y1)))) -> c9(MARK(2nd(cons1(from(y0), y1)))) MARK(s(2nd(cons1(cons(y0, y1), y2)))) -> c9(MARK(2nd(cons1(cons(y0, y1), y2)))) MARK(s(2nd(cons1(s(y0), y1)))) -> c9(MARK(2nd(cons1(s(y0), y1)))) MARK(s(2nd(cons1(cons1(y0, y1), y2)))) -> c9(MARK(2nd(cons1(cons1(y0, y1), y2)))) MARK(s(2nd(cons1(y0, y1)))) -> c9(MARK(2nd(cons1(y0, y1)))) MARK(s(2nd(cons1(y0, s(y1))))) -> c9(MARK(2nd(cons1(y0, s(y1))))) MARK(s(2nd(cons1(y0, cons1(y1, y2))))) -> c9(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(s(from(cons(y0, y1)))) -> c9(MARK(from(cons(y0, y1)))) MARK(s(from(s(y0)))) -> c9(MARK(from(s(y0)))) MARK(s(from(cons1(y0, y1)))) -> c9(MARK(from(cons1(y0, y1)))) MARK(s(from(2nd(y0)))) -> c9(MARK(from(2nd(y0)))) MARK(s(from(2nd(2nd(y0))))) -> c9(MARK(from(2nd(2nd(y0))))) MARK(s(from(2nd(from(y0))))) -> c9(MARK(from(2nd(from(y0))))) MARK(s(from(2nd(cons(y0, y1))))) -> c9(MARK(from(2nd(cons(y0, y1))))) MARK(s(from(2nd(s(y0))))) -> c9(MARK(from(2nd(s(y0))))) MARK(s(from(2nd(cons1(y0, y1))))) -> c9(MARK(from(2nd(cons1(y0, y1))))) MARK(s(from(from(y0)))) -> c9(MARK(from(from(y0)))) MARK(s(from(from(2nd(y0))))) -> c9(MARK(from(from(2nd(y0))))) MARK(s(from(from(from(y0))))) -> c9(MARK(from(from(from(y0))))) MARK(s(from(from(cons(y0, y1))))) -> c9(MARK(from(from(cons(y0, y1))))) MARK(s(from(from(s(y0))))) -> c9(MARK(from(from(s(y0))))) MARK(s(from(from(cons1(y0, y1))))) -> c9(MARK(from(from(cons1(y0, y1))))) MARK(s(cons(cons(y0, y1), y2))) -> c9(MARK(cons(cons(y0, y1), y2))) MARK(s(cons(s(y0), y1))) -> c9(MARK(cons(s(y0), y1))) MARK(s(cons(cons1(y0, y1), y2))) -> c9(MARK(cons(cons1(y0, y1), y2))) MARK(s(cons(2nd(cons(y0, y1)), y2))) -> c9(MARK(cons(2nd(cons(y0, y1)), y2))) MARK(s(cons(2nd(s(y0)), y1))) -> c9(MARK(cons(2nd(s(y0)), y1))) MARK(s(cons(2nd(2nd(2nd(y0))), y1))) -> c9(MARK(cons(2nd(2nd(2nd(y0))), y1))) MARK(s(cons(2nd(2nd(from(y0))), y1))) -> c9(MARK(cons(2nd(2nd(from(y0))), y1))) MARK(s(cons(2nd(2nd(cons(y0, y1))), y2))) -> c9(MARK(cons(2nd(2nd(cons(y0, y1))), y2))) MARK(s(cons(2nd(2nd(s(y0))), y1))) -> c9(MARK(cons(2nd(2nd(s(y0))), y1))) MARK(s(cons(2nd(2nd(cons1(y0, y1))), y2))) -> c9(MARK(cons(2nd(2nd(cons1(y0, y1))), y2))) MARK(s(cons(2nd(2nd(y0)), y1))) -> c9(MARK(cons(2nd(2nd(y0)), y1))) MARK(s(cons(2nd(from(y0)), y1))) -> c9(MARK(cons(2nd(from(y0)), y1))) MARK(s(cons(2nd(from(2nd(y0))), y1))) -> c9(MARK(cons(2nd(from(2nd(y0))), y1))) MARK(s(cons(2nd(from(from(y0))), y1))) -> c9(MARK(cons(2nd(from(from(y0))), y1))) MARK(s(cons(2nd(from(cons(y0, y1))), y2))) -> c9(MARK(cons(2nd(from(cons(y0, y1))), y2))) MARK(s(cons(2nd(from(s(y0))), y1))) -> c9(MARK(cons(2nd(from(s(y0))), y1))) MARK(s(cons(2nd(from(cons1(y0, y1))), y2))) -> c9(MARK(cons(2nd(from(cons1(y0, y1))), y2))) MARK(s(cons(2nd(cons1(y0, 2nd(y1))), y2))) -> c9(MARK(cons(2nd(cons1(y0, 2nd(y1))), y2))) MARK(s(cons(2nd(cons1(y0, from(y1))), y2))) -> c9(MARK(cons(2nd(cons1(y0, from(y1))), y2))) MARK(s(cons(2nd(cons1(y0, cons(y1, y2))), y3))) -> c9(MARK(cons(2nd(cons1(y0, cons(y1, y2))), y3))) MARK(s(cons(2nd(cons1(2nd(y0), y1)), y2))) -> c9(MARK(cons(2nd(cons1(2nd(y0), y1)), y2))) MARK(s(cons(2nd(cons1(from(y0), y1)), y2))) -> c9(MARK(cons(2nd(cons1(from(y0), y1)), y2))) MARK(s(cons(2nd(cons1(cons(y0, y1), y2)), y3))) -> c9(MARK(cons(2nd(cons1(cons(y0, y1), y2)), y3))) MARK(s(cons(2nd(cons1(s(y0), y1)), y2))) -> c9(MARK(cons(2nd(cons1(s(y0), y1)), y2))) MARK(s(cons(2nd(cons1(cons1(y0, y1), y2)), y3))) -> c9(MARK(cons(2nd(cons1(cons1(y0, y1), y2)), y3))) MARK(s(cons(2nd(cons1(y0, y1)), y2))) -> c9(MARK(cons(2nd(cons1(y0, y1)), y2))) MARK(s(cons(2nd(cons1(y0, s(y1))), y2))) -> c9(MARK(cons(2nd(cons1(y0, s(y1))), y2))) MARK(s(cons(2nd(cons1(y0, cons1(y1, y2))), y3))) -> c9(MARK(cons(2nd(cons1(y0, cons1(y1, y2))), y3))) MARK(s(cons(from(cons(y0, y1)), y2))) -> c9(MARK(cons(from(cons(y0, y1)), y2))) MARK(s(cons(from(s(y0)), y1))) -> c9(MARK(cons(from(s(y0)), y1))) MARK(s(cons(from(cons1(y0, y1)), y2))) -> c9(MARK(cons(from(cons1(y0, y1)), y2))) MARK(s(cons(from(2nd(y0)), y1))) -> c9(MARK(cons(from(2nd(y0)), y1))) MARK(s(cons(from(2nd(2nd(y0))), y1))) -> c9(MARK(cons(from(2nd(2nd(y0))), y1))) MARK(s(cons(from(2nd(from(y0))), y1))) -> c9(MARK(cons(from(2nd(from(y0))), y1))) MARK(s(cons(from(2nd(cons(y0, y1))), y2))) -> c9(MARK(cons(from(2nd(cons(y0, y1))), y2))) MARK(s(cons(from(2nd(s(y0))), y1))) -> c9(MARK(cons(from(2nd(s(y0))), y1))) MARK(s(cons(from(2nd(cons1(y0, y1))), y2))) -> c9(MARK(cons(from(2nd(cons1(y0, y1))), y2))) MARK(s(cons(from(from(y0)), y1))) -> c9(MARK(cons(from(from(y0)), y1))) MARK(s(cons(from(from(2nd(y0))), y1))) -> c9(MARK(cons(from(from(2nd(y0))), y1))) MARK(s(cons(from(from(from(y0))), y1))) -> c9(MARK(cons(from(from(from(y0))), y1))) MARK(s(cons(from(from(cons(y0, y1))), y2))) -> c9(MARK(cons(from(from(cons(y0, y1))), y2))) MARK(s(cons(from(from(s(y0))), y1))) -> c9(MARK(cons(from(from(s(y0))), y1))) MARK(s(cons(from(from(cons1(y0, y1))), y2))) -> c9(MARK(cons(from(from(cons1(y0, y1))), y2))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: MARK_1, A__2ND_1, A__FROM_1 Compound Symbols: c10_1, c11_1, c1_1, c2_1, c6_2, c6_1, c1_2, c2_2, c_1, c4_1, c7_2, c8_1, c9_1 ---------------------------------------- (123) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(cons1(z0, z1)) -> c10(MARK(z0)) by MARK(cons1(cons1(y0, y1), z1)) -> c10(MARK(cons1(y0, y1))) MARK(cons1(2nd(cons(y0, y1)), z1)) -> c10(MARK(2nd(cons(y0, y1)))) MARK(cons1(2nd(s(y0)), z1)) -> c10(MARK(2nd(s(y0)))) MARK(cons1(2nd(2nd(2nd(y0))), z1)) -> c10(MARK(2nd(2nd(2nd(y0))))) MARK(cons1(2nd(2nd(from(y0))), z1)) -> c10(MARK(2nd(2nd(from(y0))))) MARK(cons1(2nd(2nd(cons(y0, y1))), z1)) -> c10(MARK(2nd(2nd(cons(y0, y1))))) MARK(cons1(2nd(2nd(s(y0))), z1)) -> c10(MARK(2nd(2nd(s(y0))))) MARK(cons1(2nd(2nd(cons1(y0, y1))), z1)) -> c10(MARK(2nd(2nd(cons1(y0, y1))))) MARK(cons1(2nd(2nd(y0)), z1)) -> c10(MARK(2nd(2nd(y0)))) MARK(cons1(2nd(from(y0)), z1)) -> c10(MARK(2nd(from(y0)))) MARK(cons1(2nd(from(2nd(y0))), z1)) -> c10(MARK(2nd(from(2nd(y0))))) MARK(cons1(2nd(from(from(y0))), z1)) -> c10(MARK(2nd(from(from(y0))))) MARK(cons1(2nd(from(cons(y0, y1))), z1)) -> c10(MARK(2nd(from(cons(y0, y1))))) MARK(cons1(2nd(from(s(y0))), z1)) -> c10(MARK(2nd(from(s(y0))))) MARK(cons1(2nd(from(cons1(y0, y1))), z1)) -> c10(MARK(2nd(from(cons1(y0, y1))))) MARK(cons1(2nd(cons1(y0, 2nd(y1))), z1)) -> c10(MARK(2nd(cons1(y0, 2nd(y1))))) MARK(cons1(2nd(cons1(y0, from(y1))), z1)) -> c10(MARK(2nd(cons1(y0, from(y1))))) MARK(cons1(2nd(cons1(y0, cons(y1, y2))), z1)) -> c10(MARK(2nd(cons1(y0, cons(y1, y2))))) MARK(cons1(2nd(cons1(2nd(y0), y1)), z1)) -> c10(MARK(2nd(cons1(2nd(y0), y1)))) MARK(cons1(2nd(cons1(from(y0), y1)), z1)) -> c10(MARK(2nd(cons1(from(y0), y1)))) MARK(cons1(2nd(cons1(cons(y0, y1), y2)), z1)) -> c10(MARK(2nd(cons1(cons(y0, y1), y2)))) MARK(cons1(2nd(cons1(s(y0), y1)), z1)) -> c10(MARK(2nd(cons1(s(y0), y1)))) MARK(cons1(2nd(cons1(cons1(y0, y1), y2)), z1)) -> c10(MARK(2nd(cons1(cons1(y0, y1), y2)))) MARK(cons1(2nd(cons1(y0, y1)), z1)) -> c10(MARK(2nd(cons1(y0, y1)))) MARK(cons1(2nd(cons1(y0, s(y1))), z1)) -> c10(MARK(2nd(cons1(y0, s(y1))))) MARK(cons1(2nd(cons1(y0, cons1(y1, y2))), z1)) -> c10(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(cons1(from(cons(y0, y1)), z1)) -> c10(MARK(from(cons(y0, y1)))) MARK(cons1(from(s(y0)), z1)) -> c10(MARK(from(s(y0)))) MARK(cons1(from(cons1(y0, y1)), z1)) -> c10(MARK(from(cons1(y0, y1)))) MARK(cons1(from(2nd(y0)), z1)) -> c10(MARK(from(2nd(y0)))) MARK(cons1(from(2nd(2nd(y0))), z1)) -> c10(MARK(from(2nd(2nd(y0))))) MARK(cons1(from(2nd(from(y0))), z1)) -> c10(MARK(from(2nd(from(y0))))) MARK(cons1(from(2nd(cons(y0, y1))), z1)) -> c10(MARK(from(2nd(cons(y0, y1))))) MARK(cons1(from(2nd(s(y0))), z1)) -> c10(MARK(from(2nd(s(y0))))) MARK(cons1(from(2nd(cons1(y0, y1))), z1)) -> c10(MARK(from(2nd(cons1(y0, y1))))) MARK(cons1(from(from(y0)), z1)) -> c10(MARK(from(from(y0)))) MARK(cons1(from(from(2nd(y0))), z1)) -> c10(MARK(from(from(2nd(y0))))) MARK(cons1(from(from(from(y0))), z1)) -> c10(MARK(from(from(from(y0))))) MARK(cons1(from(from(cons(y0, y1))), z1)) -> c10(MARK(from(from(cons(y0, y1))))) MARK(cons1(from(from(s(y0))), z1)) -> c10(MARK(from(from(s(y0))))) MARK(cons1(from(from(cons1(y0, y1))), z1)) -> c10(MARK(from(from(cons1(y0, y1))))) MARK(cons1(cons(cons(y0, y1), y2), z1)) -> c10(MARK(cons(cons(y0, y1), y2))) MARK(cons1(cons(s(y0), y1), z1)) -> c10(MARK(cons(s(y0), y1))) MARK(cons1(cons(cons1(y0, y1), y2), z1)) -> c10(MARK(cons(cons1(y0, y1), y2))) MARK(cons1(cons(2nd(cons(y0, y1)), y2), z1)) -> c10(MARK(cons(2nd(cons(y0, y1)), y2))) MARK(cons1(cons(2nd(s(y0)), y1), z1)) -> c10(MARK(cons(2nd(s(y0)), y1))) MARK(cons1(cons(2nd(2nd(2nd(y0))), y1), z1)) -> c10(MARK(cons(2nd(2nd(2nd(y0))), y1))) MARK(cons1(cons(2nd(2nd(from(y0))), y1), z1)) -> c10(MARK(cons(2nd(2nd(from(y0))), y1))) MARK(cons1(cons(2nd(2nd(cons(y0, y1))), y2), z1)) -> c10(MARK(cons(2nd(2nd(cons(y0, y1))), y2))) MARK(cons1(cons(2nd(2nd(s(y0))), y1), z1)) -> c10(MARK(cons(2nd(2nd(s(y0))), y1))) MARK(cons1(cons(2nd(2nd(cons1(y0, y1))), y2), z1)) -> c10(MARK(cons(2nd(2nd(cons1(y0, y1))), y2))) MARK(cons1(cons(2nd(2nd(y0)), y1), z1)) -> c10(MARK(cons(2nd(2nd(y0)), y1))) MARK(cons1(cons(2nd(from(y0)), y1), z1)) -> c10(MARK(cons(2nd(from(y0)), y1))) MARK(cons1(cons(2nd(from(2nd(y0))), y1), z1)) -> c10(MARK(cons(2nd(from(2nd(y0))), y1))) MARK(cons1(cons(2nd(from(from(y0))), y1), z1)) -> c10(MARK(cons(2nd(from(from(y0))), y1))) MARK(cons1(cons(2nd(from(cons(y0, y1))), y2), z1)) -> c10(MARK(cons(2nd(from(cons(y0, y1))), y2))) MARK(cons1(cons(2nd(from(s(y0))), y1), z1)) -> c10(MARK(cons(2nd(from(s(y0))), y1))) MARK(cons1(cons(2nd(from(cons1(y0, y1))), y2), z1)) -> c10(MARK(cons(2nd(from(cons1(y0, y1))), y2))) MARK(cons1(cons(2nd(cons1(y0, 2nd(y1))), y2), z1)) -> c10(MARK(cons(2nd(cons1(y0, 2nd(y1))), y2))) MARK(cons1(cons(2nd(cons1(y0, from(y1))), y2), z1)) -> c10(MARK(cons(2nd(cons1(y0, from(y1))), y2))) MARK(cons1(cons(2nd(cons1(y0, cons(y1, y2))), y3), z1)) -> c10(MARK(cons(2nd(cons1(y0, cons(y1, y2))), y3))) MARK(cons1(cons(2nd(cons1(2nd(y0), y1)), y2), z1)) -> c10(MARK(cons(2nd(cons1(2nd(y0), y1)), y2))) MARK(cons1(cons(2nd(cons1(from(y0), y1)), y2), z1)) -> c10(MARK(cons(2nd(cons1(from(y0), y1)), y2))) MARK(cons1(cons(2nd(cons1(cons(y0, y1), y2)), y3), z1)) -> c10(MARK(cons(2nd(cons1(cons(y0, y1), y2)), y3))) MARK(cons1(cons(2nd(cons1(s(y0), y1)), y2), z1)) -> c10(MARK(cons(2nd(cons1(s(y0), y1)), y2))) MARK(cons1(cons(2nd(cons1(cons1(y0, y1), y2)), y3), z1)) -> c10(MARK(cons(2nd(cons1(cons1(y0, y1), y2)), y3))) MARK(cons1(cons(2nd(cons1(y0, y1)), y2), z1)) -> c10(MARK(cons(2nd(cons1(y0, y1)), y2))) MARK(cons1(cons(2nd(cons1(y0, s(y1))), y2), z1)) -> c10(MARK(cons(2nd(cons1(y0, s(y1))), y2))) MARK(cons1(cons(2nd(cons1(y0, cons1(y1, y2))), y3), z1)) -> c10(MARK(cons(2nd(cons1(y0, cons1(y1, y2))), y3))) MARK(cons1(cons(from(cons(y0, y1)), y2), z1)) -> c10(MARK(cons(from(cons(y0, y1)), y2))) MARK(cons1(cons(from(s(y0)), y1), z1)) -> c10(MARK(cons(from(s(y0)), y1))) MARK(cons1(cons(from(cons1(y0, y1)), y2), z1)) -> c10(MARK(cons(from(cons1(y0, y1)), y2))) MARK(cons1(cons(from(2nd(y0)), y1), z1)) -> c10(MARK(cons(from(2nd(y0)), y1))) MARK(cons1(cons(from(2nd(2nd(y0))), y1), z1)) -> c10(MARK(cons(from(2nd(2nd(y0))), y1))) MARK(cons1(cons(from(2nd(from(y0))), y1), z1)) -> c10(MARK(cons(from(2nd(from(y0))), y1))) MARK(cons1(cons(from(2nd(cons(y0, y1))), y2), z1)) -> c10(MARK(cons(from(2nd(cons(y0, y1))), y2))) MARK(cons1(cons(from(2nd(s(y0))), y1), z1)) -> c10(MARK(cons(from(2nd(s(y0))), y1))) MARK(cons1(cons(from(2nd(cons1(y0, y1))), y2), z1)) -> c10(MARK(cons(from(2nd(cons1(y0, y1))), y2))) MARK(cons1(cons(from(from(y0)), y1), z1)) -> c10(MARK(cons(from(from(y0)), y1))) MARK(cons1(cons(from(from(2nd(y0))), y1), z1)) -> c10(MARK(cons(from(from(2nd(y0))), y1))) MARK(cons1(cons(from(from(from(y0))), y1), z1)) -> c10(MARK(cons(from(from(from(y0))), y1))) MARK(cons1(cons(from(from(cons(y0, y1))), y2), z1)) -> c10(MARK(cons(from(from(cons(y0, y1))), y2))) MARK(cons1(cons(from(from(s(y0))), y1), z1)) -> c10(MARK(cons(from(from(s(y0))), y1))) MARK(cons1(cons(from(from(cons1(y0, y1))), y2), z1)) -> c10(MARK(cons(from(from(cons1(y0, y1))), y2))) MARK(cons1(s(s(y0)), z1)) -> c10(MARK(s(s(y0)))) MARK(cons1(s(cons1(y0, y1)), z1)) -> c10(MARK(s(cons1(y0, y1)))) MARK(cons1(s(2nd(cons(y0, y1))), z1)) -> c10(MARK(s(2nd(cons(y0, y1))))) MARK(cons1(s(2nd(s(y0))), z1)) -> c10(MARK(s(2nd(s(y0))))) MARK(cons1(s(2nd(2nd(2nd(y0)))), z1)) -> c10(MARK(s(2nd(2nd(2nd(y0)))))) MARK(cons1(s(2nd(2nd(from(y0)))), z1)) -> c10(MARK(s(2nd(2nd(from(y0)))))) MARK(cons1(s(2nd(2nd(cons(y0, y1)))), z1)) -> c10(MARK(s(2nd(2nd(cons(y0, y1)))))) MARK(cons1(s(2nd(2nd(s(y0)))), z1)) -> c10(MARK(s(2nd(2nd(s(y0)))))) MARK(cons1(s(2nd(2nd(cons1(y0, y1)))), z1)) -> c10(MARK(s(2nd(2nd(cons1(y0, y1)))))) MARK(cons1(s(2nd(2nd(y0))), z1)) -> c10(MARK(s(2nd(2nd(y0))))) MARK(cons1(s(2nd(from(y0))), z1)) -> c10(MARK(s(2nd(from(y0))))) MARK(cons1(s(2nd(from(2nd(y0)))), z1)) -> c10(MARK(s(2nd(from(2nd(y0)))))) MARK(cons1(s(2nd(from(from(y0)))), z1)) -> c10(MARK(s(2nd(from(from(y0)))))) MARK(cons1(s(2nd(from(cons(y0, y1)))), z1)) -> c10(MARK(s(2nd(from(cons(y0, y1)))))) MARK(cons1(s(2nd(from(s(y0)))), z1)) -> c10(MARK(s(2nd(from(s(y0)))))) MARK(cons1(s(2nd(from(cons1(y0, y1)))), z1)) -> c10(MARK(s(2nd(from(cons1(y0, y1)))))) MARK(cons1(s(2nd(cons1(y0, 2nd(y1)))), z1)) -> c10(MARK(s(2nd(cons1(y0, 2nd(y1)))))) MARK(cons1(s(2nd(cons1(y0, from(y1)))), z1)) -> c10(MARK(s(2nd(cons1(y0, from(y1)))))) MARK(cons1(s(2nd(cons1(y0, cons(y1, y2)))), z1)) -> c10(MARK(s(2nd(cons1(y0, cons(y1, y2)))))) MARK(cons1(s(2nd(cons1(2nd(y0), y1))), z1)) -> c10(MARK(s(2nd(cons1(2nd(y0), y1))))) MARK(cons1(s(2nd(cons1(from(y0), y1))), z1)) -> c10(MARK(s(2nd(cons1(from(y0), y1))))) MARK(cons1(s(2nd(cons1(cons(y0, y1), y2))), z1)) -> c10(MARK(s(2nd(cons1(cons(y0, y1), y2))))) MARK(cons1(s(2nd(cons1(s(y0), y1))), z1)) -> c10(MARK(s(2nd(cons1(s(y0), y1))))) MARK(cons1(s(2nd(cons1(cons1(y0, y1), y2))), z1)) -> c10(MARK(s(2nd(cons1(cons1(y0, y1), y2))))) MARK(cons1(s(2nd(cons1(y0, y1))), z1)) -> c10(MARK(s(2nd(cons1(y0, y1))))) MARK(cons1(s(2nd(cons1(y0, s(y1)))), z1)) -> c10(MARK(s(2nd(cons1(y0, s(y1)))))) MARK(cons1(s(2nd(cons1(y0, cons1(y1, y2)))), z1)) -> c10(MARK(s(2nd(cons1(y0, cons1(y1, y2)))))) MARK(cons1(s(from(cons(y0, y1))), z1)) -> c10(MARK(s(from(cons(y0, y1))))) MARK(cons1(s(from(s(y0))), z1)) -> c10(MARK(s(from(s(y0))))) MARK(cons1(s(from(cons1(y0, y1))), z1)) -> c10(MARK(s(from(cons1(y0, y1))))) MARK(cons1(s(from(2nd(y0))), z1)) -> c10(MARK(s(from(2nd(y0))))) MARK(cons1(s(from(2nd(2nd(y0)))), z1)) -> c10(MARK(s(from(2nd(2nd(y0)))))) MARK(cons1(s(from(2nd(from(y0)))), z1)) -> c10(MARK(s(from(2nd(from(y0)))))) MARK(cons1(s(from(2nd(cons(y0, y1)))), z1)) -> c10(MARK(s(from(2nd(cons(y0, y1)))))) MARK(cons1(s(from(2nd(s(y0)))), z1)) -> c10(MARK(s(from(2nd(s(y0)))))) MARK(cons1(s(from(2nd(cons1(y0, y1)))), z1)) -> c10(MARK(s(from(2nd(cons1(y0, y1)))))) MARK(cons1(s(from(from(y0))), z1)) -> c10(MARK(s(from(from(y0))))) MARK(cons1(s(from(from(2nd(y0)))), z1)) -> c10(MARK(s(from(from(2nd(y0)))))) MARK(cons1(s(from(from(from(y0)))), z1)) -> c10(MARK(s(from(from(from(y0)))))) MARK(cons1(s(from(from(cons(y0, y1)))), z1)) -> c10(MARK(s(from(from(cons(y0, y1)))))) MARK(cons1(s(from(from(s(y0)))), z1)) -> c10(MARK(s(from(from(s(y0)))))) MARK(cons1(s(from(from(cons1(y0, y1)))), z1)) -> c10(MARK(s(from(from(cons1(y0, y1)))))) MARK(cons1(s(cons(cons(y0, y1), y2)), z1)) -> c10(MARK(s(cons(cons(y0, y1), y2)))) MARK(cons1(s(cons(s(y0), y1)), z1)) -> c10(MARK(s(cons(s(y0), y1)))) MARK(cons1(s(cons(cons1(y0, y1), y2)), z1)) -> c10(MARK(s(cons(cons1(y0, y1), y2)))) MARK(cons1(s(cons(2nd(cons(y0, y1)), y2)), z1)) -> c10(MARK(s(cons(2nd(cons(y0, y1)), y2)))) MARK(cons1(s(cons(2nd(s(y0)), y1)), z1)) -> c10(MARK(s(cons(2nd(s(y0)), y1)))) MARK(cons1(s(cons(2nd(2nd(2nd(y0))), y1)), z1)) -> c10(MARK(s(cons(2nd(2nd(2nd(y0))), y1)))) MARK(cons1(s(cons(2nd(2nd(from(y0))), y1)), z1)) -> c10(MARK(s(cons(2nd(2nd(from(y0))), y1)))) MARK(cons1(s(cons(2nd(2nd(cons(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(2nd(cons(y0, y1))), y2)))) MARK(cons1(s(cons(2nd(2nd(s(y0))), y1)), z1)) -> c10(MARK(s(cons(2nd(2nd(s(y0))), y1)))) MARK(cons1(s(cons(2nd(2nd(cons1(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(2nd(cons1(y0, y1))), y2)))) MARK(cons1(s(cons(2nd(2nd(y0)), y1)), z1)) -> c10(MARK(s(cons(2nd(2nd(y0)), y1)))) MARK(cons1(s(cons(2nd(from(y0)), y1)), z1)) -> c10(MARK(s(cons(2nd(from(y0)), y1)))) MARK(cons1(s(cons(2nd(from(2nd(y0))), y1)), z1)) -> c10(MARK(s(cons(2nd(from(2nd(y0))), y1)))) MARK(cons1(s(cons(2nd(from(from(y0))), y1)), z1)) -> c10(MARK(s(cons(2nd(from(from(y0))), y1)))) MARK(cons1(s(cons(2nd(from(cons(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(from(cons(y0, y1))), y2)))) MARK(cons1(s(cons(2nd(from(s(y0))), y1)), z1)) -> c10(MARK(s(cons(2nd(from(s(y0))), y1)))) MARK(cons1(s(cons(2nd(from(cons1(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(from(cons1(y0, y1))), y2)))) MARK(cons1(s(cons(2nd(cons1(y0, 2nd(y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(cons1(y0, 2nd(y1))), y2)))) MARK(cons1(s(cons(2nd(cons1(y0, from(y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(cons1(y0, from(y1))), y2)))) MARK(cons1(s(cons(2nd(cons1(y0, cons(y1, y2))), y3)), z1)) -> c10(MARK(s(cons(2nd(cons1(y0, cons(y1, y2))), y3)))) MARK(cons1(s(cons(2nd(cons1(2nd(y0), y1)), y2)), z1)) -> c10(MARK(s(cons(2nd(cons1(2nd(y0), y1)), y2)))) MARK(cons1(s(cons(2nd(cons1(from(y0), y1)), y2)), z1)) -> c10(MARK(s(cons(2nd(cons1(from(y0), y1)), y2)))) MARK(cons1(s(cons(2nd(cons1(cons(y0, y1), y2)), y3)), z1)) -> c10(MARK(s(cons(2nd(cons1(cons(y0, y1), y2)), y3)))) MARK(cons1(s(cons(2nd(cons1(s(y0), y1)), y2)), z1)) -> c10(MARK(s(cons(2nd(cons1(s(y0), y1)), y2)))) MARK(cons1(s(cons(2nd(cons1(cons1(y0, y1), y2)), y3)), z1)) -> c10(MARK(s(cons(2nd(cons1(cons1(y0, y1), y2)), y3)))) MARK(cons1(s(cons(2nd(cons1(y0, y1)), y2)), z1)) -> c10(MARK(s(cons(2nd(cons1(y0, y1)), y2)))) MARK(cons1(s(cons(2nd(cons1(y0, s(y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(cons1(y0, s(y1))), y2)))) MARK(cons1(s(cons(2nd(cons1(y0, cons1(y1, y2))), y3)), z1)) -> c10(MARK(s(cons(2nd(cons1(y0, cons1(y1, y2))), y3)))) MARK(cons1(s(cons(from(cons(y0, y1)), y2)), z1)) -> c10(MARK(s(cons(from(cons(y0, y1)), y2)))) MARK(cons1(s(cons(from(s(y0)), y1)), z1)) -> c10(MARK(s(cons(from(s(y0)), y1)))) MARK(cons1(s(cons(from(cons1(y0, y1)), y2)), z1)) -> c10(MARK(s(cons(from(cons1(y0, y1)), y2)))) MARK(cons1(s(cons(from(2nd(y0)), y1)), z1)) -> c10(MARK(s(cons(from(2nd(y0)), y1)))) MARK(cons1(s(cons(from(2nd(2nd(y0))), y1)), z1)) -> c10(MARK(s(cons(from(2nd(2nd(y0))), y1)))) MARK(cons1(s(cons(from(2nd(from(y0))), y1)), z1)) -> c10(MARK(s(cons(from(2nd(from(y0))), y1)))) MARK(cons1(s(cons(from(2nd(cons(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(from(2nd(cons(y0, y1))), y2)))) MARK(cons1(s(cons(from(2nd(s(y0))), y1)), z1)) -> c10(MARK(s(cons(from(2nd(s(y0))), y1)))) MARK(cons1(s(cons(from(2nd(cons1(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(from(2nd(cons1(y0, y1))), y2)))) MARK(cons1(s(cons(from(from(y0)), y1)), z1)) -> c10(MARK(s(cons(from(from(y0)), y1)))) MARK(cons1(s(cons(from(from(2nd(y0))), y1)), z1)) -> c10(MARK(s(cons(from(from(2nd(y0))), y1)))) MARK(cons1(s(cons(from(from(from(y0))), y1)), z1)) -> c10(MARK(s(cons(from(from(from(y0))), y1)))) MARK(cons1(s(cons(from(from(cons(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(from(from(cons(y0, y1))), y2)))) MARK(cons1(s(cons(from(from(s(y0))), y1)), z1)) -> c10(MARK(s(cons(from(from(s(y0))), y1)))) MARK(cons1(s(cons(from(from(cons1(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(from(from(cons1(y0, y1))), y2)))) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) MARK(2nd(cons1(x0, 2nd(z0)))) -> c6(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(cons1(x0, 2nd(z0)))) MARK(2nd(cons1(x0, from(z0)))) -> c6(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(cons1(x0, from(z0)))) MARK(2nd(cons1(x0, cons(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons1(x0, cons(z0, z1)))) MARK(2nd(cons1(2nd(z0), x1))) -> c6(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(cons1(2nd(z0), x1))) MARK(2nd(cons1(from(z0), x1))) -> c6(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(cons1(from(z0), x1))) MARK(2nd(cons1(cons(z0, z1), x1))) -> c6(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons1(cons(z0, z1), x1))) MARK(2nd(cons1(s(z0), x1))) -> c6(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(cons1(s(z0), x1))) MARK(2nd(cons1(cons1(z0, z1), x1))) -> c6(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(cons1(z0, z1), x1))) MARK(2nd(cons1(x0, x1))) -> c6(MARK(cons1(x0, x1))) MARK(2nd(cons1(x0, s(z0)))) -> c6(MARK(cons1(x0, s(z0)))) MARK(2nd(cons1(x0, cons1(z0, z1)))) -> c6(MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons1(z0, cons(from(y0), z2))) -> c(MARK(from(y0))) A__2ND(cons1(z0, cons(cons(y0, y1), z2))) -> c(MARK(cons(y0, y1))) A__2ND(cons1(z0, cons(s(y0), z2))) -> c(MARK(s(y0))) A__2ND(cons1(z0, cons(cons1(y0, y1), z2))) -> c(MARK(cons1(y0, y1))) A__2ND(cons1(z0, cons(2nd(cons(y0, y1)), z2))) -> c(MARK(2nd(cons(y0, y1)))) A__2ND(cons1(z0, cons(2nd(s(y0)), z2))) -> c(MARK(2nd(s(y0)))) A__2ND(cons1(z0, cons(2nd(2nd(2nd(y0))), z2))) -> c(MARK(2nd(2nd(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(from(y0))), z2))) -> c(MARK(2nd(2nd(from(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(s(y0))), z2))) -> c(MARK(2nd(2nd(s(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons1(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(y0)), z2))) -> c(MARK(2nd(2nd(y0)))) A__2ND(cons1(z0, cons(2nd(from(y0)), z2))) -> c(MARK(2nd(from(y0)))) A__2ND(cons1(z0, cons(2nd(from(2nd(y0))), z2))) -> c(MARK(2nd(from(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(from(from(y0))), z2))) -> c(MARK(2nd(from(from(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons(y0, y1))), z2))) -> c(MARK(2nd(from(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(from(s(y0))), z2))) -> c(MARK(2nd(from(s(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons1(y0, y1))), z2))) -> c(MARK(2nd(from(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, 2nd(y1))), z2))) -> c(MARK(2nd(cons1(y0, 2nd(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, from(y1))), z2))) -> c(MARK(2nd(cons1(y0, from(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons(y1, y2))))) A__2ND(cons1(z0, cons(2nd(cons1(2nd(y0), y1)), z2))) -> c(MARK(2nd(cons1(2nd(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(from(y0), y1)), z2))) -> c(MARK(2nd(cons1(from(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(s(y0), y1)), z2))) -> c(MARK(2nd(cons1(s(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons1(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, y1)), z2))) -> c(MARK(2nd(cons1(y0, y1)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, s(y1))), z2))) -> c(MARK(2nd(cons1(y0, s(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons1(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons1(y1, y2))))) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(from(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(x0)) A__2ND(cons(x0, cons(s(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(x0)) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(cons(2nd(z0), x2))) A__2ND(cons(x0, cons(from(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(cons(from(z0), x2))) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(cons(cons(z0, z1), x2))) A__2ND(cons(x0, cons(s(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(cons(s(z0), x2))) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(cons(cons1(z0, z1), x2))) A__2ND(cons(x0, cons(x1, x2))) -> c2(MARK(cons(x1, x2))) A__FROM(from(y0)) -> c4(MARK(from(y0))) A__FROM(cons(y0, y1)) -> c4(MARK(cons(y0, y1))) A__FROM(s(y0)) -> c4(MARK(s(y0))) A__FROM(cons1(y0, y1)) -> c4(MARK(cons1(y0, y1))) A__FROM(2nd(cons(y0, y1))) -> c4(MARK(2nd(cons(y0, y1)))) A__FROM(2nd(s(y0))) -> c4(MARK(2nd(s(y0)))) A__FROM(2nd(2nd(2nd(y0)))) -> c4(MARK(2nd(2nd(2nd(y0))))) A__FROM(2nd(2nd(from(y0)))) -> c4(MARK(2nd(2nd(from(y0))))) A__FROM(2nd(2nd(cons(y0, y1)))) -> c4(MARK(2nd(2nd(cons(y0, y1))))) A__FROM(2nd(2nd(s(y0)))) -> c4(MARK(2nd(2nd(s(y0))))) A__FROM(2nd(2nd(cons1(y0, y1)))) -> c4(MARK(2nd(2nd(cons1(y0, y1))))) A__FROM(2nd(2nd(y0))) -> c4(MARK(2nd(2nd(y0)))) A__FROM(2nd(from(y0))) -> c4(MARK(2nd(from(y0)))) A__FROM(2nd(from(2nd(y0)))) -> c4(MARK(2nd(from(2nd(y0))))) A__FROM(2nd(from(from(y0)))) -> c4(MARK(2nd(from(from(y0))))) A__FROM(2nd(from(cons(y0, y1)))) -> c4(MARK(2nd(from(cons(y0, y1))))) A__FROM(2nd(from(s(y0)))) -> c4(MARK(2nd(from(s(y0))))) A__FROM(2nd(from(cons1(y0, y1)))) -> c4(MARK(2nd(from(cons1(y0, y1))))) A__FROM(2nd(cons1(y0, 2nd(y1)))) -> c4(MARK(2nd(cons1(y0, 2nd(y1))))) A__FROM(2nd(cons1(y0, from(y1)))) -> c4(MARK(2nd(cons1(y0, from(y1))))) A__FROM(2nd(cons1(y0, cons(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons(y1, y2))))) A__FROM(2nd(cons1(2nd(y0), y1))) -> c4(MARK(2nd(cons1(2nd(y0), y1)))) A__FROM(2nd(cons1(from(y0), y1))) -> c4(MARK(2nd(cons1(from(y0), y1)))) A__FROM(2nd(cons1(cons(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons(y0, y1), y2)))) A__FROM(2nd(cons1(s(y0), y1))) -> c4(MARK(2nd(cons1(s(y0), y1)))) A__FROM(2nd(cons1(cons1(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__FROM(2nd(cons1(y0, y1))) -> c4(MARK(2nd(cons1(y0, y1)))) A__FROM(2nd(cons1(y0, s(y1)))) -> c4(MARK(2nd(cons1(y0, s(y1))))) A__FROM(2nd(cons1(y0, cons1(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons1(z0, z1))) -> c7(A__FROM(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(from(2nd(x0))) -> c7(A__FROM(2nd(mark(x0))), MARK(2nd(x0))) MARK(from(2nd(2nd(z0)))) -> c7(A__FROM(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(from(2nd(from(z0)))) -> c7(A__FROM(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(from(2nd(cons(z0, z1)))) -> c7(A__FROM(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(from(2nd(s(z0)))) -> c7(A__FROM(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(from(2nd(cons1(z0, z1)))) -> c7(A__FROM(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(from(from(x0))) -> c7(A__FROM(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(from(from(x0))) -> c7(A__FROM(from(mark(x0))), MARK(from(x0))) MARK(from(from(2nd(z0)))) -> c7(A__FROM(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(from(from(from(z0)))) -> c7(A__FROM(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(from(from(cons(z0, z1)))) -> c7(A__FROM(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(from(from(s(z0)))) -> c7(A__FROM(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(from(from(cons1(z0, z1)))) -> c7(A__FROM(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(cons(cons(y0, y1), z1)) -> c8(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c8(MARK(s(y0))) MARK(cons(cons1(y0, y1), z1)) -> c8(MARK(cons1(y0, y1))) MARK(cons(2nd(cons(y0, y1)), z1)) -> c8(MARK(2nd(cons(y0, y1)))) MARK(cons(2nd(s(y0)), z1)) -> c8(MARK(2nd(s(y0)))) MARK(cons(2nd(2nd(2nd(y0))), z1)) -> c8(MARK(2nd(2nd(2nd(y0))))) MARK(cons(2nd(2nd(from(y0))), z1)) -> c8(MARK(2nd(2nd(from(y0))))) MARK(cons(2nd(2nd(cons(y0, y1))), z1)) -> c8(MARK(2nd(2nd(cons(y0, y1))))) MARK(cons(2nd(2nd(s(y0))), z1)) -> c8(MARK(2nd(2nd(s(y0))))) MARK(cons(2nd(2nd(cons1(y0, y1))), z1)) -> c8(MARK(2nd(2nd(cons1(y0, y1))))) MARK(cons(2nd(2nd(y0)), z1)) -> c8(MARK(2nd(2nd(y0)))) MARK(cons(2nd(from(y0)), z1)) -> c8(MARK(2nd(from(y0)))) MARK(cons(2nd(from(2nd(y0))), z1)) -> c8(MARK(2nd(from(2nd(y0))))) MARK(cons(2nd(from(from(y0))), z1)) -> c8(MARK(2nd(from(from(y0))))) MARK(cons(2nd(from(cons(y0, y1))), z1)) -> c8(MARK(2nd(from(cons(y0, y1))))) MARK(cons(2nd(from(s(y0))), z1)) -> c8(MARK(2nd(from(s(y0))))) MARK(cons(2nd(from(cons1(y0, y1))), z1)) -> c8(MARK(2nd(from(cons1(y0, y1))))) MARK(cons(2nd(cons1(y0, 2nd(y1))), z1)) -> c8(MARK(2nd(cons1(y0, 2nd(y1))))) MARK(cons(2nd(cons1(y0, from(y1))), z1)) -> c8(MARK(2nd(cons1(y0, from(y1))))) MARK(cons(2nd(cons1(y0, cons(y1, y2))), z1)) -> c8(MARK(2nd(cons1(y0, cons(y1, y2))))) MARK(cons(2nd(cons1(2nd(y0), y1)), z1)) -> c8(MARK(2nd(cons1(2nd(y0), y1)))) MARK(cons(2nd(cons1(from(y0), y1)), z1)) -> c8(MARK(2nd(cons1(from(y0), y1)))) MARK(cons(2nd(cons1(cons(y0, y1), y2)), z1)) -> c8(MARK(2nd(cons1(cons(y0, y1), y2)))) MARK(cons(2nd(cons1(s(y0), y1)), z1)) -> c8(MARK(2nd(cons1(s(y0), y1)))) MARK(cons(2nd(cons1(cons1(y0, y1), y2)), z1)) -> c8(MARK(2nd(cons1(cons1(y0, y1), y2)))) MARK(cons(2nd(cons1(y0, y1)), z1)) -> c8(MARK(2nd(cons1(y0, y1)))) MARK(cons(2nd(cons1(y0, s(y1))), z1)) -> c8(MARK(2nd(cons1(y0, s(y1))))) MARK(cons(2nd(cons1(y0, cons1(y1, y2))), z1)) -> c8(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(cons(from(cons(y0, y1)), z1)) -> c8(MARK(from(cons(y0, y1)))) MARK(cons(from(s(y0)), z1)) -> c8(MARK(from(s(y0)))) MARK(cons(from(cons1(y0, y1)), z1)) -> c8(MARK(from(cons1(y0, y1)))) MARK(cons(from(2nd(y0)), z1)) -> c8(MARK(from(2nd(y0)))) MARK(cons(from(2nd(2nd(y0))), z1)) -> c8(MARK(from(2nd(2nd(y0))))) MARK(cons(from(2nd(from(y0))), z1)) -> c8(MARK(from(2nd(from(y0))))) MARK(cons(from(2nd(cons(y0, y1))), z1)) -> c8(MARK(from(2nd(cons(y0, y1))))) MARK(cons(from(2nd(s(y0))), z1)) -> c8(MARK(from(2nd(s(y0))))) MARK(cons(from(2nd(cons1(y0, y1))), z1)) -> c8(MARK(from(2nd(cons1(y0, y1))))) MARK(cons(from(from(y0)), z1)) -> c8(MARK(from(from(y0)))) MARK(cons(from(from(2nd(y0))), z1)) -> c8(MARK(from(from(2nd(y0))))) MARK(cons(from(from(from(y0))), z1)) -> c8(MARK(from(from(from(y0))))) MARK(cons(from(from(cons(y0, y1))), z1)) -> c8(MARK(from(from(cons(y0, y1))))) MARK(cons(from(from(s(y0))), z1)) -> c8(MARK(from(from(s(y0))))) MARK(cons(from(from(cons1(y0, y1))), z1)) -> c8(MARK(from(from(cons1(y0, y1))))) MARK(s(s(y0))) -> c9(MARK(s(y0))) MARK(s(cons1(y0, y1))) -> c9(MARK(cons1(y0, y1))) MARK(s(2nd(cons(y0, y1)))) -> c9(MARK(2nd(cons(y0, y1)))) MARK(s(2nd(s(y0)))) -> c9(MARK(2nd(s(y0)))) MARK(s(2nd(2nd(2nd(y0))))) -> c9(MARK(2nd(2nd(2nd(y0))))) MARK(s(2nd(2nd(from(y0))))) -> c9(MARK(2nd(2nd(from(y0))))) MARK(s(2nd(2nd(cons(y0, y1))))) -> c9(MARK(2nd(2nd(cons(y0, y1))))) MARK(s(2nd(2nd(s(y0))))) -> c9(MARK(2nd(2nd(s(y0))))) MARK(s(2nd(2nd(cons1(y0, y1))))) -> c9(MARK(2nd(2nd(cons1(y0, y1))))) MARK(s(2nd(2nd(y0)))) -> c9(MARK(2nd(2nd(y0)))) MARK(s(2nd(from(y0)))) -> c9(MARK(2nd(from(y0)))) MARK(s(2nd(from(2nd(y0))))) -> c9(MARK(2nd(from(2nd(y0))))) MARK(s(2nd(from(from(y0))))) -> c9(MARK(2nd(from(from(y0))))) MARK(s(2nd(from(cons(y0, y1))))) -> c9(MARK(2nd(from(cons(y0, y1))))) MARK(s(2nd(from(s(y0))))) -> c9(MARK(2nd(from(s(y0))))) MARK(s(2nd(from(cons1(y0, y1))))) -> c9(MARK(2nd(from(cons1(y0, y1))))) MARK(s(2nd(cons1(y0, 2nd(y1))))) -> c9(MARK(2nd(cons1(y0, 2nd(y1))))) MARK(s(2nd(cons1(y0, from(y1))))) -> c9(MARK(2nd(cons1(y0, from(y1))))) MARK(s(2nd(cons1(y0, cons(y1, y2))))) -> c9(MARK(2nd(cons1(y0, cons(y1, y2))))) MARK(s(2nd(cons1(2nd(y0), y1)))) -> c9(MARK(2nd(cons1(2nd(y0), y1)))) MARK(s(2nd(cons1(from(y0), y1)))) -> c9(MARK(2nd(cons1(from(y0), y1)))) MARK(s(2nd(cons1(cons(y0, y1), y2)))) -> c9(MARK(2nd(cons1(cons(y0, y1), y2)))) MARK(s(2nd(cons1(s(y0), y1)))) -> c9(MARK(2nd(cons1(s(y0), y1)))) MARK(s(2nd(cons1(cons1(y0, y1), y2)))) -> c9(MARK(2nd(cons1(cons1(y0, y1), y2)))) MARK(s(2nd(cons1(y0, y1)))) -> c9(MARK(2nd(cons1(y0, y1)))) MARK(s(2nd(cons1(y0, s(y1))))) -> c9(MARK(2nd(cons1(y0, s(y1))))) MARK(s(2nd(cons1(y0, cons1(y1, y2))))) -> c9(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(s(from(cons(y0, y1)))) -> c9(MARK(from(cons(y0, y1)))) MARK(s(from(s(y0)))) -> c9(MARK(from(s(y0)))) MARK(s(from(cons1(y0, y1)))) -> c9(MARK(from(cons1(y0, y1)))) MARK(s(from(2nd(y0)))) -> c9(MARK(from(2nd(y0)))) MARK(s(from(2nd(2nd(y0))))) -> c9(MARK(from(2nd(2nd(y0))))) MARK(s(from(2nd(from(y0))))) -> c9(MARK(from(2nd(from(y0))))) MARK(s(from(2nd(cons(y0, y1))))) -> c9(MARK(from(2nd(cons(y0, y1))))) MARK(s(from(2nd(s(y0))))) -> c9(MARK(from(2nd(s(y0))))) MARK(s(from(2nd(cons1(y0, y1))))) -> c9(MARK(from(2nd(cons1(y0, y1))))) MARK(s(from(from(y0)))) -> c9(MARK(from(from(y0)))) MARK(s(from(from(2nd(y0))))) -> c9(MARK(from(from(2nd(y0))))) MARK(s(from(from(from(y0))))) -> c9(MARK(from(from(from(y0))))) MARK(s(from(from(cons(y0, y1))))) -> c9(MARK(from(from(cons(y0, y1))))) MARK(s(from(from(s(y0))))) -> c9(MARK(from(from(s(y0))))) MARK(s(from(from(cons1(y0, y1))))) -> c9(MARK(from(from(cons1(y0, y1))))) MARK(s(cons(cons(y0, y1), y2))) -> c9(MARK(cons(cons(y0, y1), y2))) MARK(s(cons(s(y0), y1))) -> c9(MARK(cons(s(y0), y1))) MARK(s(cons(cons1(y0, y1), y2))) -> c9(MARK(cons(cons1(y0, y1), y2))) MARK(s(cons(2nd(cons(y0, y1)), y2))) -> c9(MARK(cons(2nd(cons(y0, y1)), y2))) MARK(s(cons(2nd(s(y0)), y1))) -> c9(MARK(cons(2nd(s(y0)), y1))) MARK(s(cons(2nd(2nd(2nd(y0))), y1))) -> c9(MARK(cons(2nd(2nd(2nd(y0))), y1))) MARK(s(cons(2nd(2nd(from(y0))), y1))) -> c9(MARK(cons(2nd(2nd(from(y0))), y1))) MARK(s(cons(2nd(2nd(cons(y0, y1))), y2))) -> c9(MARK(cons(2nd(2nd(cons(y0, y1))), y2))) MARK(s(cons(2nd(2nd(s(y0))), y1))) -> c9(MARK(cons(2nd(2nd(s(y0))), y1))) MARK(s(cons(2nd(2nd(cons1(y0, y1))), y2))) -> c9(MARK(cons(2nd(2nd(cons1(y0, y1))), y2))) MARK(s(cons(2nd(2nd(y0)), y1))) -> c9(MARK(cons(2nd(2nd(y0)), y1))) MARK(s(cons(2nd(from(y0)), y1))) -> c9(MARK(cons(2nd(from(y0)), y1))) MARK(s(cons(2nd(from(2nd(y0))), y1))) -> c9(MARK(cons(2nd(from(2nd(y0))), y1))) MARK(s(cons(2nd(from(from(y0))), y1))) -> c9(MARK(cons(2nd(from(from(y0))), y1))) MARK(s(cons(2nd(from(cons(y0, y1))), y2))) -> c9(MARK(cons(2nd(from(cons(y0, y1))), y2))) MARK(s(cons(2nd(from(s(y0))), y1))) -> c9(MARK(cons(2nd(from(s(y0))), y1))) MARK(s(cons(2nd(from(cons1(y0, y1))), y2))) -> c9(MARK(cons(2nd(from(cons1(y0, y1))), y2))) MARK(s(cons(2nd(cons1(y0, 2nd(y1))), y2))) -> c9(MARK(cons(2nd(cons1(y0, 2nd(y1))), y2))) MARK(s(cons(2nd(cons1(y0, from(y1))), y2))) -> c9(MARK(cons(2nd(cons1(y0, from(y1))), y2))) MARK(s(cons(2nd(cons1(y0, cons(y1, y2))), y3))) -> c9(MARK(cons(2nd(cons1(y0, cons(y1, y2))), y3))) MARK(s(cons(2nd(cons1(2nd(y0), y1)), y2))) -> c9(MARK(cons(2nd(cons1(2nd(y0), y1)), y2))) MARK(s(cons(2nd(cons1(from(y0), y1)), y2))) -> c9(MARK(cons(2nd(cons1(from(y0), y1)), y2))) MARK(s(cons(2nd(cons1(cons(y0, y1), y2)), y3))) -> c9(MARK(cons(2nd(cons1(cons(y0, y1), y2)), y3))) MARK(s(cons(2nd(cons1(s(y0), y1)), y2))) -> c9(MARK(cons(2nd(cons1(s(y0), y1)), y2))) MARK(s(cons(2nd(cons1(cons1(y0, y1), y2)), y3))) -> c9(MARK(cons(2nd(cons1(cons1(y0, y1), y2)), y3))) MARK(s(cons(2nd(cons1(y0, y1)), y2))) -> c9(MARK(cons(2nd(cons1(y0, y1)), y2))) MARK(s(cons(2nd(cons1(y0, s(y1))), y2))) -> c9(MARK(cons(2nd(cons1(y0, s(y1))), y2))) MARK(s(cons(2nd(cons1(y0, cons1(y1, y2))), y3))) -> c9(MARK(cons(2nd(cons1(y0, cons1(y1, y2))), y3))) MARK(s(cons(from(cons(y0, y1)), y2))) -> c9(MARK(cons(from(cons(y0, y1)), y2))) MARK(s(cons(from(s(y0)), y1))) -> c9(MARK(cons(from(s(y0)), y1))) MARK(s(cons(from(cons1(y0, y1)), y2))) -> c9(MARK(cons(from(cons1(y0, y1)), y2))) MARK(s(cons(from(2nd(y0)), y1))) -> c9(MARK(cons(from(2nd(y0)), y1))) MARK(s(cons(from(2nd(2nd(y0))), y1))) -> c9(MARK(cons(from(2nd(2nd(y0))), y1))) MARK(s(cons(from(2nd(from(y0))), y1))) -> c9(MARK(cons(from(2nd(from(y0))), y1))) MARK(s(cons(from(2nd(cons(y0, y1))), y2))) -> c9(MARK(cons(from(2nd(cons(y0, y1))), y2))) MARK(s(cons(from(2nd(s(y0))), y1))) -> c9(MARK(cons(from(2nd(s(y0))), y1))) MARK(s(cons(from(2nd(cons1(y0, y1))), y2))) -> c9(MARK(cons(from(2nd(cons1(y0, y1))), y2))) MARK(s(cons(from(from(y0)), y1))) -> 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MARK(cons1(2nd(2nd(y0)), z1)) -> c10(MARK(2nd(2nd(y0)))) MARK(cons1(2nd(from(y0)), z1)) -> c10(MARK(2nd(from(y0)))) MARK(cons1(2nd(from(2nd(y0))), z1)) -> c10(MARK(2nd(from(2nd(y0))))) MARK(cons1(2nd(from(from(y0))), z1)) -> c10(MARK(2nd(from(from(y0))))) MARK(cons1(2nd(from(cons(y0, y1))), z1)) -> c10(MARK(2nd(from(cons(y0, y1))))) MARK(cons1(2nd(from(s(y0))), z1)) -> c10(MARK(2nd(from(s(y0))))) MARK(cons1(2nd(from(cons1(y0, y1))), z1)) -> c10(MARK(2nd(from(cons1(y0, y1))))) MARK(cons1(2nd(cons1(y0, 2nd(y1))), z1)) -> c10(MARK(2nd(cons1(y0, 2nd(y1))))) MARK(cons1(2nd(cons1(y0, from(y1))), z1)) -> c10(MARK(2nd(cons1(y0, from(y1))))) MARK(cons1(2nd(cons1(y0, cons(y1, y2))), z1)) -> c10(MARK(2nd(cons1(y0, cons(y1, y2))))) MARK(cons1(2nd(cons1(2nd(y0), y1)), z1)) -> c10(MARK(2nd(cons1(2nd(y0), y1)))) MARK(cons1(2nd(cons1(from(y0), y1)), z1)) -> c10(MARK(2nd(cons1(from(y0), y1)))) MARK(cons1(2nd(cons1(cons(y0, y1), y2)), z1)) -> c10(MARK(2nd(cons1(cons(y0, y1), y2)))) MARK(cons1(2nd(cons1(s(y0), y1)), z1)) -> c10(MARK(2nd(cons1(s(y0), y1)))) MARK(cons1(2nd(cons1(cons1(y0, y1), y2)), z1)) -> c10(MARK(2nd(cons1(cons1(y0, y1), y2)))) MARK(cons1(2nd(cons1(y0, y1)), z1)) -> c10(MARK(2nd(cons1(y0, y1)))) MARK(cons1(2nd(cons1(y0, s(y1))), z1)) -> c10(MARK(2nd(cons1(y0, s(y1))))) MARK(cons1(2nd(cons1(y0, cons1(y1, y2))), z1)) -> c10(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(cons1(from(cons(y0, y1)), z1)) -> c10(MARK(from(cons(y0, y1)))) MARK(cons1(from(s(y0)), z1)) -> c10(MARK(from(s(y0)))) MARK(cons1(from(cons1(y0, y1)), z1)) -> c10(MARK(from(cons1(y0, y1)))) MARK(cons1(from(2nd(y0)), z1)) -> c10(MARK(from(2nd(y0)))) MARK(cons1(from(2nd(2nd(y0))), z1)) -> c10(MARK(from(2nd(2nd(y0))))) MARK(cons1(from(2nd(from(y0))), z1)) -> c10(MARK(from(2nd(from(y0))))) MARK(cons1(from(2nd(cons(y0, y1))), z1)) -> c10(MARK(from(2nd(cons(y0, y1))))) MARK(cons1(from(2nd(s(y0))), z1)) -> c10(MARK(from(2nd(s(y0))))) MARK(cons1(from(2nd(cons1(y0, y1))), z1)) -> c10(MARK(from(2nd(cons1(y0, y1))))) MARK(cons1(from(from(y0)), z1)) -> c10(MARK(from(from(y0)))) MARK(cons1(from(from(2nd(y0))), z1)) -> c10(MARK(from(from(2nd(y0))))) MARK(cons1(from(from(from(y0))), z1)) -> c10(MARK(from(from(from(y0))))) MARK(cons1(from(from(cons(y0, y1))), z1)) -> c10(MARK(from(from(cons(y0, y1))))) MARK(cons1(from(from(s(y0))), z1)) -> c10(MARK(from(from(s(y0))))) MARK(cons1(from(from(cons1(y0, y1))), z1)) -> c10(MARK(from(from(cons1(y0, y1))))) MARK(cons1(cons(cons(y0, y1), y2), z1)) -> c10(MARK(cons(cons(y0, y1), y2))) MARK(cons1(cons(s(y0), y1), z1)) -> c10(MARK(cons(s(y0), y1))) MARK(cons1(cons(cons1(y0, y1), y2), z1)) -> c10(MARK(cons(cons1(y0, y1), y2))) MARK(cons1(cons(2nd(cons(y0, y1)), y2), z1)) -> c10(MARK(cons(2nd(cons(y0, y1)), y2))) MARK(cons1(cons(2nd(s(y0)), y1), z1)) -> c10(MARK(cons(2nd(s(y0)), y1))) MARK(cons1(cons(2nd(2nd(2nd(y0))), y1), z1)) -> c10(MARK(cons(2nd(2nd(2nd(y0))), y1))) MARK(cons1(cons(2nd(2nd(from(y0))), y1), z1)) -> c10(MARK(cons(2nd(2nd(from(y0))), y1))) MARK(cons1(cons(2nd(2nd(cons(y0, y1))), y2), z1)) -> c10(MARK(cons(2nd(2nd(cons(y0, y1))), y2))) MARK(cons1(cons(2nd(2nd(s(y0))), y1), z1)) -> c10(MARK(cons(2nd(2nd(s(y0))), y1))) MARK(cons1(cons(2nd(2nd(cons1(y0, y1))), y2), z1)) -> c10(MARK(cons(2nd(2nd(cons1(y0, y1))), y2))) MARK(cons1(cons(2nd(2nd(y0)), y1), z1)) -> c10(MARK(cons(2nd(2nd(y0)), y1))) MARK(cons1(cons(2nd(from(y0)), y1), z1)) -> c10(MARK(cons(2nd(from(y0)), y1))) MARK(cons1(cons(2nd(from(2nd(y0))), y1), z1)) -> c10(MARK(cons(2nd(from(2nd(y0))), y1))) MARK(cons1(cons(2nd(from(from(y0))), y1), z1)) -> c10(MARK(cons(2nd(from(from(y0))), y1))) MARK(cons1(cons(2nd(from(cons(y0, y1))), y2), z1)) -> c10(MARK(cons(2nd(from(cons(y0, y1))), y2))) MARK(cons1(cons(2nd(from(s(y0))), y1), z1)) -> c10(MARK(cons(2nd(from(s(y0))), y1))) MARK(cons1(cons(2nd(from(cons1(y0, y1))), y2), z1)) -> c10(MARK(cons(2nd(from(cons1(y0, y1))), y2))) MARK(cons1(cons(2nd(cons1(y0, 2nd(y1))), y2), z1)) -> c10(MARK(cons(2nd(cons1(y0, 2nd(y1))), y2))) MARK(cons1(cons(2nd(cons1(y0, from(y1))), y2), z1)) -> c10(MARK(cons(2nd(cons1(y0, from(y1))), y2))) MARK(cons1(cons(2nd(cons1(y0, cons(y1, y2))), y3), z1)) -> c10(MARK(cons(2nd(cons1(y0, cons(y1, y2))), y3))) MARK(cons1(cons(2nd(cons1(2nd(y0), y1)), y2), z1)) -> c10(MARK(cons(2nd(cons1(2nd(y0), y1)), y2))) MARK(cons1(cons(2nd(cons1(from(y0), y1)), y2), z1)) -> c10(MARK(cons(2nd(cons1(from(y0), y1)), y2))) MARK(cons1(cons(2nd(cons1(cons(y0, y1), y2)), y3), z1)) -> c10(MARK(cons(2nd(cons1(cons(y0, y1), y2)), y3))) MARK(cons1(cons(2nd(cons1(s(y0), y1)), y2), z1)) -> c10(MARK(cons(2nd(cons1(s(y0), y1)), y2))) MARK(cons1(cons(2nd(cons1(cons1(y0, y1), y2)), y3), z1)) -> c10(MARK(cons(2nd(cons1(cons1(y0, y1), y2)), y3))) MARK(cons1(cons(2nd(cons1(y0, y1)), y2), z1)) -> c10(MARK(cons(2nd(cons1(y0, y1)), y2))) MARK(cons1(cons(2nd(cons1(y0, s(y1))), y2), z1)) -> c10(MARK(cons(2nd(cons1(y0, s(y1))), y2))) MARK(cons1(cons(2nd(cons1(y0, cons1(y1, y2))), y3), z1)) -> c10(MARK(cons(2nd(cons1(y0, cons1(y1, y2))), y3))) MARK(cons1(cons(from(cons(y0, y1)), y2), z1)) -> c10(MARK(cons(from(cons(y0, y1)), y2))) MARK(cons1(cons(from(s(y0)), y1), z1)) -> c10(MARK(cons(from(s(y0)), y1))) MARK(cons1(cons(from(cons1(y0, y1)), y2), z1)) -> c10(MARK(cons(from(cons1(y0, y1)), y2))) MARK(cons1(cons(from(2nd(y0)), y1), z1)) -> c10(MARK(cons(from(2nd(y0)), y1))) MARK(cons1(cons(from(2nd(2nd(y0))), y1), z1)) -> c10(MARK(cons(from(2nd(2nd(y0))), y1))) MARK(cons1(cons(from(2nd(from(y0))), y1), z1)) -> c10(MARK(cons(from(2nd(from(y0))), y1))) MARK(cons1(cons(from(2nd(cons(y0, y1))), y2), z1)) -> c10(MARK(cons(from(2nd(cons(y0, y1))), y2))) MARK(cons1(cons(from(2nd(s(y0))), y1), z1)) -> c10(MARK(cons(from(2nd(s(y0))), y1))) MARK(cons1(cons(from(2nd(cons1(y0, y1))), y2), z1)) -> c10(MARK(cons(from(2nd(cons1(y0, y1))), y2))) MARK(cons1(cons(from(from(y0)), y1), z1)) -> c10(MARK(cons(from(from(y0)), y1))) MARK(cons1(cons(from(from(2nd(y0))), y1), z1)) -> c10(MARK(cons(from(from(2nd(y0))), y1))) MARK(cons1(cons(from(from(from(y0))), y1), z1)) -> c10(MARK(cons(from(from(from(y0))), y1))) MARK(cons1(cons(from(from(cons(y0, y1))), y2), z1)) -> c10(MARK(cons(from(from(cons(y0, y1))), y2))) MARK(cons1(cons(from(from(s(y0))), y1), z1)) -> c10(MARK(cons(from(from(s(y0))), y1))) MARK(cons1(cons(from(from(cons1(y0, y1))), y2), z1)) -> c10(MARK(cons(from(from(cons1(y0, y1))), y2))) MARK(cons1(s(s(y0)), z1)) -> c10(MARK(s(s(y0)))) MARK(cons1(s(cons1(y0, y1)), z1)) -> c10(MARK(s(cons1(y0, y1)))) MARK(cons1(s(2nd(cons(y0, y1))), z1)) -> c10(MARK(s(2nd(cons(y0, y1))))) MARK(cons1(s(2nd(s(y0))), z1)) -> c10(MARK(s(2nd(s(y0))))) MARK(cons1(s(2nd(2nd(2nd(y0)))), z1)) -> c10(MARK(s(2nd(2nd(2nd(y0)))))) MARK(cons1(s(2nd(2nd(from(y0)))), z1)) -> c10(MARK(s(2nd(2nd(from(y0)))))) MARK(cons1(s(2nd(2nd(cons(y0, y1)))), z1)) -> c10(MARK(s(2nd(2nd(cons(y0, y1)))))) MARK(cons1(s(2nd(2nd(s(y0)))), z1)) -> c10(MARK(s(2nd(2nd(s(y0)))))) MARK(cons1(s(2nd(2nd(cons1(y0, y1)))), z1)) -> c10(MARK(s(2nd(2nd(cons1(y0, y1)))))) MARK(cons1(s(2nd(2nd(y0))), z1)) -> c10(MARK(s(2nd(2nd(y0))))) MARK(cons1(s(2nd(from(y0))), z1)) -> c10(MARK(s(2nd(from(y0))))) MARK(cons1(s(2nd(from(2nd(y0)))), z1)) -> c10(MARK(s(2nd(from(2nd(y0)))))) MARK(cons1(s(2nd(from(from(y0)))), z1)) -> c10(MARK(s(2nd(from(from(y0)))))) MARK(cons1(s(2nd(from(cons(y0, y1)))), z1)) -> c10(MARK(s(2nd(from(cons(y0, y1)))))) MARK(cons1(s(2nd(from(s(y0)))), z1)) -> c10(MARK(s(2nd(from(s(y0)))))) MARK(cons1(s(2nd(from(cons1(y0, y1)))), z1)) -> c10(MARK(s(2nd(from(cons1(y0, y1)))))) MARK(cons1(s(2nd(cons1(y0, 2nd(y1)))), z1)) -> c10(MARK(s(2nd(cons1(y0, 2nd(y1)))))) MARK(cons1(s(2nd(cons1(y0, from(y1)))), z1)) -> c10(MARK(s(2nd(cons1(y0, from(y1)))))) MARK(cons1(s(2nd(cons1(y0, cons(y1, y2)))), z1)) -> c10(MARK(s(2nd(cons1(y0, cons(y1, y2)))))) MARK(cons1(s(2nd(cons1(2nd(y0), y1))), z1)) -> c10(MARK(s(2nd(cons1(2nd(y0), y1))))) MARK(cons1(s(2nd(cons1(from(y0), y1))), z1)) -> c10(MARK(s(2nd(cons1(from(y0), y1))))) MARK(cons1(s(2nd(cons1(cons(y0, y1), y2))), z1)) -> c10(MARK(s(2nd(cons1(cons(y0, y1), y2))))) MARK(cons1(s(2nd(cons1(s(y0), y1))), z1)) -> c10(MARK(s(2nd(cons1(s(y0), y1))))) MARK(cons1(s(2nd(cons1(cons1(y0, y1), y2))), z1)) -> c10(MARK(s(2nd(cons1(cons1(y0, y1), y2))))) MARK(cons1(s(2nd(cons1(y0, y1))), z1)) -> c10(MARK(s(2nd(cons1(y0, y1))))) MARK(cons1(s(2nd(cons1(y0, s(y1)))), z1)) -> c10(MARK(s(2nd(cons1(y0, s(y1)))))) MARK(cons1(s(2nd(cons1(y0, cons1(y1, y2)))), z1)) -> c10(MARK(s(2nd(cons1(y0, cons1(y1, y2)))))) MARK(cons1(s(from(cons(y0, y1))), z1)) -> c10(MARK(s(from(cons(y0, y1))))) MARK(cons1(s(from(s(y0))), z1)) -> c10(MARK(s(from(s(y0))))) MARK(cons1(s(from(cons1(y0, y1))), z1)) -> c10(MARK(s(from(cons1(y0, y1))))) MARK(cons1(s(from(2nd(y0))), z1)) -> c10(MARK(s(from(2nd(y0))))) MARK(cons1(s(from(2nd(2nd(y0)))), z1)) -> c10(MARK(s(from(2nd(2nd(y0)))))) MARK(cons1(s(from(2nd(from(y0)))), z1)) -> c10(MARK(s(from(2nd(from(y0)))))) MARK(cons1(s(from(2nd(cons(y0, y1)))), z1)) -> c10(MARK(s(from(2nd(cons(y0, y1)))))) MARK(cons1(s(from(2nd(s(y0)))), z1)) -> c10(MARK(s(from(2nd(s(y0)))))) MARK(cons1(s(from(2nd(cons1(y0, y1)))), z1)) -> c10(MARK(s(from(2nd(cons1(y0, y1)))))) MARK(cons1(s(from(from(y0))), z1)) -> c10(MARK(s(from(from(y0))))) MARK(cons1(s(from(from(2nd(y0)))), z1)) -> c10(MARK(s(from(from(2nd(y0)))))) MARK(cons1(s(from(from(from(y0)))), z1)) -> c10(MARK(s(from(from(from(y0)))))) MARK(cons1(s(from(from(cons(y0, y1)))), z1)) -> c10(MARK(s(from(from(cons(y0, y1)))))) MARK(cons1(s(from(from(s(y0)))), z1)) -> c10(MARK(s(from(from(s(y0)))))) MARK(cons1(s(from(from(cons1(y0, y1)))), z1)) -> c10(MARK(s(from(from(cons1(y0, y1)))))) MARK(cons1(s(cons(cons(y0, y1), y2)), z1)) -> c10(MARK(s(cons(cons(y0, y1), y2)))) MARK(cons1(s(cons(s(y0), y1)), z1)) -> c10(MARK(s(cons(s(y0), y1)))) MARK(cons1(s(cons(cons1(y0, y1), y2)), z1)) -> c10(MARK(s(cons(cons1(y0, y1), y2)))) MARK(cons1(s(cons(2nd(cons(y0, y1)), y2)), z1)) -> c10(MARK(s(cons(2nd(cons(y0, y1)), y2)))) MARK(cons1(s(cons(2nd(s(y0)), y1)), z1)) -> c10(MARK(s(cons(2nd(s(y0)), y1)))) MARK(cons1(s(cons(2nd(2nd(2nd(y0))), y1)), z1)) -> c10(MARK(s(cons(2nd(2nd(2nd(y0))), y1)))) MARK(cons1(s(cons(2nd(2nd(from(y0))), y1)), z1)) -> c10(MARK(s(cons(2nd(2nd(from(y0))), y1)))) MARK(cons1(s(cons(2nd(2nd(cons(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(2nd(cons(y0, y1))), y2)))) MARK(cons1(s(cons(2nd(2nd(s(y0))), y1)), z1)) -> c10(MARK(s(cons(2nd(2nd(s(y0))), y1)))) MARK(cons1(s(cons(2nd(2nd(cons1(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(2nd(cons1(y0, y1))), y2)))) MARK(cons1(s(cons(2nd(2nd(y0)), y1)), z1)) -> c10(MARK(s(cons(2nd(2nd(y0)), y1)))) MARK(cons1(s(cons(2nd(from(y0)), y1)), z1)) -> c10(MARK(s(cons(2nd(from(y0)), y1)))) MARK(cons1(s(cons(2nd(from(2nd(y0))), y1)), z1)) -> c10(MARK(s(cons(2nd(from(2nd(y0))), y1)))) MARK(cons1(s(cons(2nd(from(from(y0))), y1)), z1)) -> c10(MARK(s(cons(2nd(from(from(y0))), y1)))) MARK(cons1(s(cons(2nd(from(cons(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(from(cons(y0, y1))), y2)))) MARK(cons1(s(cons(2nd(from(s(y0))), y1)), z1)) -> c10(MARK(s(cons(2nd(from(s(y0))), y1)))) MARK(cons1(s(cons(2nd(from(cons1(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(from(cons1(y0, y1))), y2)))) MARK(cons1(s(cons(2nd(cons1(y0, 2nd(y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(cons1(y0, 2nd(y1))), y2)))) MARK(cons1(s(cons(2nd(cons1(y0, from(y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(cons1(y0, from(y1))), y2)))) MARK(cons1(s(cons(2nd(cons1(y0, cons(y1, y2))), y3)), z1)) -> c10(MARK(s(cons(2nd(cons1(y0, cons(y1, y2))), y3)))) MARK(cons1(s(cons(2nd(cons1(2nd(y0), y1)), y2)), z1)) -> c10(MARK(s(cons(2nd(cons1(2nd(y0), y1)), y2)))) MARK(cons1(s(cons(2nd(cons1(from(y0), y1)), y2)), z1)) -> c10(MARK(s(cons(2nd(cons1(from(y0), y1)), y2)))) MARK(cons1(s(cons(2nd(cons1(cons(y0, y1), y2)), y3)), z1)) -> c10(MARK(s(cons(2nd(cons1(cons(y0, y1), y2)), y3)))) MARK(cons1(s(cons(2nd(cons1(s(y0), y1)), y2)), z1)) -> c10(MARK(s(cons(2nd(cons1(s(y0), y1)), y2)))) MARK(cons1(s(cons(2nd(cons1(cons1(y0, y1), y2)), y3)), z1)) -> c10(MARK(s(cons(2nd(cons1(cons1(y0, y1), y2)), y3)))) MARK(cons1(s(cons(2nd(cons1(y0, y1)), y2)), z1)) -> c10(MARK(s(cons(2nd(cons1(y0, y1)), y2)))) MARK(cons1(s(cons(2nd(cons1(y0, s(y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(cons1(y0, s(y1))), y2)))) MARK(cons1(s(cons(2nd(cons1(y0, cons1(y1, y2))), y3)), z1)) -> c10(MARK(s(cons(2nd(cons1(y0, cons1(y1, y2))), y3)))) MARK(cons1(s(cons(from(cons(y0, y1)), y2)), z1)) -> c10(MARK(s(cons(from(cons(y0, y1)), y2)))) MARK(cons1(s(cons(from(s(y0)), y1)), z1)) -> c10(MARK(s(cons(from(s(y0)), y1)))) MARK(cons1(s(cons(from(cons1(y0, y1)), y2)), z1)) -> c10(MARK(s(cons(from(cons1(y0, y1)), y2)))) MARK(cons1(s(cons(from(2nd(y0)), y1)), z1)) -> c10(MARK(s(cons(from(2nd(y0)), y1)))) MARK(cons1(s(cons(from(2nd(2nd(y0))), y1)), z1)) -> c10(MARK(s(cons(from(2nd(2nd(y0))), y1)))) MARK(cons1(s(cons(from(2nd(from(y0))), y1)), z1)) -> c10(MARK(s(cons(from(2nd(from(y0))), y1)))) MARK(cons1(s(cons(from(2nd(cons(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(from(2nd(cons(y0, y1))), y2)))) MARK(cons1(s(cons(from(2nd(s(y0))), y1)), z1)) -> c10(MARK(s(cons(from(2nd(s(y0))), y1)))) MARK(cons1(s(cons(from(2nd(cons1(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(from(2nd(cons1(y0, y1))), y2)))) MARK(cons1(s(cons(from(from(y0)), y1)), z1)) -> c10(MARK(s(cons(from(from(y0)), y1)))) MARK(cons1(s(cons(from(from(2nd(y0))), y1)), z1)) -> c10(MARK(s(cons(from(from(2nd(y0))), y1)))) MARK(cons1(s(cons(from(from(from(y0))), y1)), z1)) -> c10(MARK(s(cons(from(from(from(y0))), y1)))) MARK(cons1(s(cons(from(from(cons(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(from(from(cons(y0, y1))), y2)))) MARK(cons1(s(cons(from(from(s(y0))), y1)), z1)) -> c10(MARK(s(cons(from(from(s(y0))), y1)))) MARK(cons1(s(cons(from(from(cons1(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(from(from(cons1(y0, y1))), y2)))) S tuples: MARK(cons1(z0, z1)) -> c11(MARK(z1)) A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) MARK(2nd(cons1(x0, 2nd(z0)))) -> c6(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(cons1(x0, 2nd(z0)))) MARK(2nd(cons1(x0, from(z0)))) -> c6(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(cons1(x0, from(z0)))) MARK(2nd(cons1(x0, cons(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons1(x0, cons(z0, z1)))) MARK(2nd(cons1(2nd(z0), x1))) -> c6(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(cons1(2nd(z0), x1))) MARK(2nd(cons1(from(z0), x1))) -> c6(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(cons1(from(z0), x1))) MARK(2nd(cons1(cons(z0, z1), x1))) -> c6(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons1(cons(z0, z1), x1))) MARK(2nd(cons1(s(z0), x1))) -> c6(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(cons1(s(z0), x1))) MARK(2nd(cons1(cons1(z0, z1), x1))) -> c6(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(cons1(z0, z1), x1))) MARK(2nd(cons1(x0, x1))) -> c6(MARK(cons1(x0, x1))) MARK(2nd(cons1(x0, s(z0)))) -> c6(MARK(cons1(x0, s(z0)))) MARK(2nd(cons1(x0, cons1(z0, z1)))) -> c6(MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons1(z0, cons(from(y0), z2))) -> c(MARK(from(y0))) A__2ND(cons1(z0, cons(cons(y0, y1), z2))) -> c(MARK(cons(y0, y1))) A__2ND(cons1(z0, cons(s(y0), z2))) -> c(MARK(s(y0))) A__2ND(cons1(z0, cons(cons1(y0, y1), z2))) -> c(MARK(cons1(y0, y1))) A__2ND(cons1(z0, cons(2nd(cons(y0, y1)), z2))) -> c(MARK(2nd(cons(y0, y1)))) A__2ND(cons1(z0, cons(2nd(s(y0)), z2))) -> c(MARK(2nd(s(y0)))) A__2ND(cons1(z0, cons(2nd(2nd(2nd(y0))), z2))) -> c(MARK(2nd(2nd(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(from(y0))), z2))) -> c(MARK(2nd(2nd(from(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(s(y0))), z2))) -> c(MARK(2nd(2nd(s(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons1(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(y0)), z2))) -> c(MARK(2nd(2nd(y0)))) A__2ND(cons1(z0, cons(2nd(from(y0)), z2))) -> c(MARK(2nd(from(y0)))) A__2ND(cons1(z0, cons(2nd(from(2nd(y0))), z2))) -> c(MARK(2nd(from(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(from(from(y0))), z2))) -> c(MARK(2nd(from(from(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons(y0, y1))), z2))) -> c(MARK(2nd(from(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(from(s(y0))), z2))) -> c(MARK(2nd(from(s(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons1(y0, y1))), z2))) -> c(MARK(2nd(from(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, 2nd(y1))), z2))) -> c(MARK(2nd(cons1(y0, 2nd(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, from(y1))), z2))) -> c(MARK(2nd(cons1(y0, from(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons(y1, y2))))) A__2ND(cons1(z0, cons(2nd(cons1(2nd(y0), y1)), z2))) -> c(MARK(2nd(cons1(2nd(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(from(y0), y1)), z2))) -> c(MARK(2nd(cons1(from(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(s(y0), y1)), z2))) -> c(MARK(2nd(cons1(s(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons1(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, y1)), z2))) -> c(MARK(2nd(cons1(y0, y1)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, s(y1))), z2))) -> c(MARK(2nd(cons1(y0, s(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons1(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons1(y1, y2))))) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(from(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(x0)) A__2ND(cons(x0, cons(s(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(x0)) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(cons(2nd(z0), x2))) A__2ND(cons(x0, cons(from(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(cons(from(z0), x2))) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(cons(cons(z0, z1), x2))) A__2ND(cons(x0, cons(s(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(cons(s(z0), x2))) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(cons(cons1(z0, z1), x2))) A__2ND(cons(x0, cons(x1, x2))) -> c2(MARK(cons(x1, x2))) A__FROM(from(y0)) -> c4(MARK(from(y0))) A__FROM(cons(y0, y1)) -> c4(MARK(cons(y0, y1))) A__FROM(s(y0)) -> c4(MARK(s(y0))) A__FROM(cons1(y0, y1)) -> c4(MARK(cons1(y0, y1))) A__FROM(2nd(cons(y0, y1))) -> c4(MARK(2nd(cons(y0, y1)))) A__FROM(2nd(s(y0))) -> c4(MARK(2nd(s(y0)))) A__FROM(2nd(2nd(2nd(y0)))) -> c4(MARK(2nd(2nd(2nd(y0))))) A__FROM(2nd(2nd(from(y0)))) -> c4(MARK(2nd(2nd(from(y0))))) A__FROM(2nd(2nd(cons(y0, y1)))) -> c4(MARK(2nd(2nd(cons(y0, y1))))) A__FROM(2nd(2nd(s(y0)))) -> c4(MARK(2nd(2nd(s(y0))))) A__FROM(2nd(2nd(cons1(y0, y1)))) -> c4(MARK(2nd(2nd(cons1(y0, y1))))) A__FROM(2nd(2nd(y0))) -> c4(MARK(2nd(2nd(y0)))) A__FROM(2nd(from(y0))) -> c4(MARK(2nd(from(y0)))) A__FROM(2nd(from(2nd(y0)))) -> c4(MARK(2nd(from(2nd(y0))))) A__FROM(2nd(from(from(y0)))) -> c4(MARK(2nd(from(from(y0))))) A__FROM(2nd(from(cons(y0, y1)))) -> c4(MARK(2nd(from(cons(y0, y1))))) A__FROM(2nd(from(s(y0)))) -> c4(MARK(2nd(from(s(y0))))) A__FROM(2nd(from(cons1(y0, y1)))) -> c4(MARK(2nd(from(cons1(y0, y1))))) A__FROM(2nd(cons1(y0, 2nd(y1)))) -> c4(MARK(2nd(cons1(y0, 2nd(y1))))) A__FROM(2nd(cons1(y0, from(y1)))) -> c4(MARK(2nd(cons1(y0, from(y1))))) A__FROM(2nd(cons1(y0, cons(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons(y1, y2))))) A__FROM(2nd(cons1(2nd(y0), y1))) -> c4(MARK(2nd(cons1(2nd(y0), y1)))) A__FROM(2nd(cons1(from(y0), y1))) -> c4(MARK(2nd(cons1(from(y0), y1)))) A__FROM(2nd(cons1(cons(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons(y0, y1), y2)))) A__FROM(2nd(cons1(s(y0), y1))) -> c4(MARK(2nd(cons1(s(y0), y1)))) A__FROM(2nd(cons1(cons1(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__FROM(2nd(cons1(y0, y1))) -> c4(MARK(2nd(cons1(y0, y1)))) A__FROM(2nd(cons1(y0, s(y1)))) -> c4(MARK(2nd(cons1(y0, s(y1))))) A__FROM(2nd(cons1(y0, cons1(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons1(z0, z1))) -> c7(A__FROM(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(from(2nd(x0))) -> c7(A__FROM(2nd(mark(x0))), MARK(2nd(x0))) MARK(from(2nd(2nd(z0)))) -> c7(A__FROM(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(from(2nd(from(z0)))) -> c7(A__FROM(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(from(2nd(cons(z0, z1)))) -> c7(A__FROM(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(from(2nd(s(z0)))) -> c7(A__FROM(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(from(2nd(cons1(z0, z1)))) -> c7(A__FROM(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(from(from(x0))) -> c7(A__FROM(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(from(from(x0))) -> c7(A__FROM(from(mark(x0))), MARK(from(x0))) MARK(from(from(2nd(z0)))) -> c7(A__FROM(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(from(from(from(z0)))) -> c7(A__FROM(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(from(from(cons(z0, z1)))) -> c7(A__FROM(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(from(from(s(z0)))) -> c7(A__FROM(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(from(from(cons1(z0, z1)))) -> c7(A__FROM(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(cons(cons(y0, y1), z1)) -> c8(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c8(MARK(s(y0))) MARK(cons(cons1(y0, y1), z1)) -> c8(MARK(cons1(y0, y1))) MARK(cons(2nd(cons(y0, y1)), z1)) -> c8(MARK(2nd(cons(y0, y1)))) MARK(cons(2nd(s(y0)), z1)) -> c8(MARK(2nd(s(y0)))) MARK(cons(2nd(2nd(2nd(y0))), z1)) -> c8(MARK(2nd(2nd(2nd(y0))))) MARK(cons(2nd(2nd(from(y0))), z1)) -> c8(MARK(2nd(2nd(from(y0))))) MARK(cons(2nd(2nd(cons(y0, y1))), z1)) -> c8(MARK(2nd(2nd(cons(y0, y1))))) MARK(cons(2nd(2nd(s(y0))), z1)) -> c8(MARK(2nd(2nd(s(y0))))) MARK(cons(2nd(2nd(cons1(y0, y1))), z1)) -> c8(MARK(2nd(2nd(cons1(y0, y1))))) MARK(cons(2nd(2nd(y0)), z1)) -> c8(MARK(2nd(2nd(y0)))) MARK(cons(2nd(from(y0)), z1)) -> c8(MARK(2nd(from(y0)))) MARK(cons(2nd(from(2nd(y0))), z1)) -> c8(MARK(2nd(from(2nd(y0))))) MARK(cons(2nd(from(from(y0))), z1)) -> c8(MARK(2nd(from(from(y0))))) MARK(cons(2nd(from(cons(y0, y1))), z1)) -> c8(MARK(2nd(from(cons(y0, y1))))) MARK(cons(2nd(from(s(y0))), z1)) -> c8(MARK(2nd(from(s(y0))))) MARK(cons(2nd(from(cons1(y0, y1))), z1)) -> c8(MARK(2nd(from(cons1(y0, y1))))) MARK(cons(2nd(cons1(y0, 2nd(y1))), z1)) -> c8(MARK(2nd(cons1(y0, 2nd(y1))))) MARK(cons(2nd(cons1(y0, from(y1))), z1)) -> c8(MARK(2nd(cons1(y0, from(y1))))) MARK(cons(2nd(cons1(y0, cons(y1, y2))), z1)) -> c8(MARK(2nd(cons1(y0, cons(y1, y2))))) MARK(cons(2nd(cons1(2nd(y0), y1)), z1)) -> c8(MARK(2nd(cons1(2nd(y0), y1)))) MARK(cons(2nd(cons1(from(y0), y1)), z1)) -> c8(MARK(2nd(cons1(from(y0), y1)))) MARK(cons(2nd(cons1(cons(y0, y1), y2)), z1)) -> c8(MARK(2nd(cons1(cons(y0, y1), y2)))) MARK(cons(2nd(cons1(s(y0), y1)), z1)) -> c8(MARK(2nd(cons1(s(y0), y1)))) MARK(cons(2nd(cons1(cons1(y0, y1), y2)), z1)) -> c8(MARK(2nd(cons1(cons1(y0, y1), y2)))) MARK(cons(2nd(cons1(y0, y1)), z1)) -> c8(MARK(2nd(cons1(y0, y1)))) MARK(cons(2nd(cons1(y0, s(y1))), z1)) -> c8(MARK(2nd(cons1(y0, s(y1))))) MARK(cons(2nd(cons1(y0, cons1(y1, y2))), z1)) -> c8(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(cons(from(cons(y0, y1)), z1)) -> c8(MARK(from(cons(y0, y1)))) MARK(cons(from(s(y0)), z1)) -> c8(MARK(from(s(y0)))) MARK(cons(from(cons1(y0, y1)), z1)) -> c8(MARK(from(cons1(y0, y1)))) MARK(cons(from(2nd(y0)), z1)) -> c8(MARK(from(2nd(y0)))) MARK(cons(from(2nd(2nd(y0))), z1)) -> c8(MARK(from(2nd(2nd(y0))))) MARK(cons(from(2nd(from(y0))), z1)) -> c8(MARK(from(2nd(from(y0))))) MARK(cons(from(2nd(cons(y0, y1))), z1)) -> c8(MARK(from(2nd(cons(y0, y1))))) MARK(cons(from(2nd(s(y0))), z1)) -> c8(MARK(from(2nd(s(y0))))) MARK(cons(from(2nd(cons1(y0, y1))), z1)) -> c8(MARK(from(2nd(cons1(y0, y1))))) MARK(cons(from(from(y0)), z1)) -> c8(MARK(from(from(y0)))) MARK(cons(from(from(2nd(y0))), z1)) -> c8(MARK(from(from(2nd(y0))))) MARK(cons(from(from(from(y0))), z1)) -> c8(MARK(from(from(from(y0))))) MARK(cons(from(from(cons(y0, y1))), z1)) -> c8(MARK(from(from(cons(y0, y1))))) MARK(cons(from(from(s(y0))), z1)) -> c8(MARK(from(from(s(y0))))) MARK(cons(from(from(cons1(y0, y1))), z1)) -> c8(MARK(from(from(cons1(y0, y1))))) MARK(s(s(y0))) -> c9(MARK(s(y0))) MARK(s(cons1(y0, y1))) -> c9(MARK(cons1(y0, y1))) MARK(s(2nd(cons(y0, y1)))) -> c9(MARK(2nd(cons(y0, y1)))) MARK(s(2nd(s(y0)))) -> c9(MARK(2nd(s(y0)))) MARK(s(2nd(2nd(2nd(y0))))) -> c9(MARK(2nd(2nd(2nd(y0))))) MARK(s(2nd(2nd(from(y0))))) -> c9(MARK(2nd(2nd(from(y0))))) MARK(s(2nd(2nd(cons(y0, y1))))) -> c9(MARK(2nd(2nd(cons(y0, y1))))) MARK(s(2nd(2nd(s(y0))))) -> c9(MARK(2nd(2nd(s(y0))))) MARK(s(2nd(2nd(cons1(y0, y1))))) -> c9(MARK(2nd(2nd(cons1(y0, y1))))) MARK(s(2nd(2nd(y0)))) -> c9(MARK(2nd(2nd(y0)))) MARK(s(2nd(from(y0)))) -> c9(MARK(2nd(from(y0)))) MARK(s(2nd(from(2nd(y0))))) -> c9(MARK(2nd(from(2nd(y0))))) MARK(s(2nd(from(from(y0))))) -> c9(MARK(2nd(from(from(y0))))) MARK(s(2nd(from(cons(y0, y1))))) -> c9(MARK(2nd(from(cons(y0, y1))))) MARK(s(2nd(from(s(y0))))) -> c9(MARK(2nd(from(s(y0))))) MARK(s(2nd(from(cons1(y0, y1))))) -> c9(MARK(2nd(from(cons1(y0, y1))))) MARK(s(2nd(cons1(y0, 2nd(y1))))) -> c9(MARK(2nd(cons1(y0, 2nd(y1))))) MARK(s(2nd(cons1(y0, from(y1))))) -> c9(MARK(2nd(cons1(y0, from(y1))))) MARK(s(2nd(cons1(y0, cons(y1, y2))))) -> c9(MARK(2nd(cons1(y0, cons(y1, y2))))) MARK(s(2nd(cons1(2nd(y0), y1)))) -> c9(MARK(2nd(cons1(2nd(y0), y1)))) MARK(s(2nd(cons1(from(y0), y1)))) -> c9(MARK(2nd(cons1(from(y0), y1)))) MARK(s(2nd(cons1(cons(y0, y1), y2)))) -> c9(MARK(2nd(cons1(cons(y0, y1), y2)))) MARK(s(2nd(cons1(s(y0), y1)))) -> c9(MARK(2nd(cons1(s(y0), y1)))) MARK(s(2nd(cons1(cons1(y0, y1), y2)))) -> c9(MARK(2nd(cons1(cons1(y0, y1), y2)))) MARK(s(2nd(cons1(y0, y1)))) -> c9(MARK(2nd(cons1(y0, y1)))) MARK(s(2nd(cons1(y0, s(y1))))) -> c9(MARK(2nd(cons1(y0, s(y1))))) MARK(s(2nd(cons1(y0, cons1(y1, y2))))) -> c9(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(s(from(cons(y0, y1)))) -> c9(MARK(from(cons(y0, y1)))) MARK(s(from(s(y0)))) -> c9(MARK(from(s(y0)))) MARK(s(from(cons1(y0, y1)))) -> c9(MARK(from(cons1(y0, y1)))) MARK(s(from(2nd(y0)))) -> c9(MARK(from(2nd(y0)))) MARK(s(from(2nd(2nd(y0))))) -> c9(MARK(from(2nd(2nd(y0))))) MARK(s(from(2nd(from(y0))))) -> c9(MARK(from(2nd(from(y0))))) MARK(s(from(2nd(cons(y0, y1))))) -> c9(MARK(from(2nd(cons(y0, y1))))) MARK(s(from(2nd(s(y0))))) -> c9(MARK(from(2nd(s(y0))))) MARK(s(from(2nd(cons1(y0, y1))))) -> c9(MARK(from(2nd(cons1(y0, y1))))) MARK(s(from(from(y0)))) -> c9(MARK(from(from(y0)))) MARK(s(from(from(2nd(y0))))) -> c9(MARK(from(from(2nd(y0))))) MARK(s(from(from(from(y0))))) -> c9(MARK(from(from(from(y0))))) MARK(s(from(from(cons(y0, y1))))) -> c9(MARK(from(from(cons(y0, y1))))) MARK(s(from(from(s(y0))))) -> c9(MARK(from(from(s(y0))))) MARK(s(from(from(cons1(y0, y1))))) -> c9(MARK(from(from(cons1(y0, y1))))) MARK(s(cons(cons(y0, y1), y2))) -> c9(MARK(cons(cons(y0, y1), y2))) MARK(s(cons(s(y0), y1))) -> c9(MARK(cons(s(y0), y1))) MARK(s(cons(cons1(y0, y1), y2))) -> c9(MARK(cons(cons1(y0, y1), y2))) MARK(s(cons(2nd(cons(y0, y1)), y2))) -> c9(MARK(cons(2nd(cons(y0, y1)), y2))) MARK(s(cons(2nd(s(y0)), y1))) -> c9(MARK(cons(2nd(s(y0)), y1))) MARK(s(cons(2nd(2nd(2nd(y0))), y1))) -> c9(MARK(cons(2nd(2nd(2nd(y0))), y1))) MARK(s(cons(2nd(2nd(from(y0))), y1))) -> c9(MARK(cons(2nd(2nd(from(y0))), y1))) MARK(s(cons(2nd(2nd(cons(y0, y1))), y2))) -> c9(MARK(cons(2nd(2nd(cons(y0, y1))), y2))) MARK(s(cons(2nd(2nd(s(y0))), y1))) -> c9(MARK(cons(2nd(2nd(s(y0))), y1))) MARK(s(cons(2nd(2nd(cons1(y0, y1))), y2))) -> c9(MARK(cons(2nd(2nd(cons1(y0, y1))), y2))) MARK(s(cons(2nd(2nd(y0)), y1))) -> c9(MARK(cons(2nd(2nd(y0)), y1))) MARK(s(cons(2nd(from(y0)), y1))) -> c9(MARK(cons(2nd(from(y0)), y1))) MARK(s(cons(2nd(from(2nd(y0))), y1))) -> c9(MARK(cons(2nd(from(2nd(y0))), y1))) MARK(s(cons(2nd(from(from(y0))), y1))) -> c9(MARK(cons(2nd(from(from(y0))), y1))) MARK(s(cons(2nd(from(cons(y0, y1))), y2))) -> c9(MARK(cons(2nd(from(cons(y0, y1))), y2))) MARK(s(cons(2nd(from(s(y0))), y1))) -> c9(MARK(cons(2nd(from(s(y0))), y1))) MARK(s(cons(2nd(from(cons1(y0, y1))), y2))) -> c9(MARK(cons(2nd(from(cons1(y0, y1))), y2))) MARK(s(cons(2nd(cons1(y0, 2nd(y1))), y2))) -> c9(MARK(cons(2nd(cons1(y0, 2nd(y1))), y2))) MARK(s(cons(2nd(cons1(y0, from(y1))), y2))) -> c9(MARK(cons(2nd(cons1(y0, from(y1))), y2))) MARK(s(cons(2nd(cons1(y0, cons(y1, y2))), y3))) -> c9(MARK(cons(2nd(cons1(y0, cons(y1, y2))), y3))) MARK(s(cons(2nd(cons1(2nd(y0), y1)), y2))) -> c9(MARK(cons(2nd(cons1(2nd(y0), y1)), y2))) MARK(s(cons(2nd(cons1(from(y0), y1)), y2))) -> c9(MARK(cons(2nd(cons1(from(y0), y1)), y2))) MARK(s(cons(2nd(cons1(cons(y0, y1), y2)), y3))) -> c9(MARK(cons(2nd(cons1(cons(y0, y1), y2)), y3))) MARK(s(cons(2nd(cons1(s(y0), y1)), y2))) -> c9(MARK(cons(2nd(cons1(s(y0), y1)), y2))) MARK(s(cons(2nd(cons1(cons1(y0, y1), y2)), y3))) -> c9(MARK(cons(2nd(cons1(cons1(y0, y1), y2)), y3))) MARK(s(cons(2nd(cons1(y0, y1)), y2))) -> c9(MARK(cons(2nd(cons1(y0, y1)), y2))) MARK(s(cons(2nd(cons1(y0, s(y1))), y2))) -> c9(MARK(cons(2nd(cons1(y0, s(y1))), y2))) MARK(s(cons(2nd(cons1(y0, cons1(y1, y2))), y3))) -> c9(MARK(cons(2nd(cons1(y0, cons1(y1, y2))), y3))) MARK(s(cons(from(cons(y0, y1)), y2))) -> c9(MARK(cons(from(cons(y0, y1)), y2))) MARK(s(cons(from(s(y0)), y1))) -> c9(MARK(cons(from(s(y0)), y1))) MARK(s(cons(from(cons1(y0, y1)), y2))) -> c9(MARK(cons(from(cons1(y0, y1)), y2))) MARK(s(cons(from(2nd(y0)), y1))) -> c9(MARK(cons(from(2nd(y0)), y1))) MARK(s(cons(from(2nd(2nd(y0))), y1))) -> c9(MARK(cons(from(2nd(2nd(y0))), y1))) MARK(s(cons(from(2nd(from(y0))), y1))) -> c9(MARK(cons(from(2nd(from(y0))), y1))) MARK(s(cons(from(2nd(cons(y0, y1))), y2))) -> c9(MARK(cons(from(2nd(cons(y0, y1))), y2))) MARK(s(cons(from(2nd(s(y0))), y1))) -> c9(MARK(cons(from(2nd(s(y0))), y1))) MARK(s(cons(from(2nd(cons1(y0, y1))), y2))) -> c9(MARK(cons(from(2nd(cons1(y0, y1))), y2))) MARK(s(cons(from(from(y0)), y1))) -> c9(MARK(cons(from(from(y0)), y1))) MARK(s(cons(from(from(2nd(y0))), y1))) -> c9(MARK(cons(from(from(2nd(y0))), y1))) MARK(s(cons(from(from(from(y0))), y1))) -> c9(MARK(cons(from(from(from(y0))), y1))) MARK(s(cons(from(from(cons(y0, y1))), y2))) -> c9(MARK(cons(from(from(cons(y0, y1))), y2))) MARK(s(cons(from(from(s(y0))), y1))) -> c9(MARK(cons(from(from(s(y0))), y1))) MARK(s(cons(from(from(cons1(y0, y1))), y2))) -> c9(MARK(cons(from(from(cons1(y0, y1))), y2))) MARK(cons1(cons1(y0, y1), z1)) -> c10(MARK(cons1(y0, y1))) MARK(cons1(2nd(cons(y0, y1)), z1)) -> c10(MARK(2nd(cons(y0, y1)))) MARK(cons1(2nd(s(y0)), z1)) -> c10(MARK(2nd(s(y0)))) MARK(cons1(2nd(2nd(2nd(y0))), z1)) -> c10(MARK(2nd(2nd(2nd(y0))))) MARK(cons1(2nd(2nd(from(y0))), z1)) -> c10(MARK(2nd(2nd(from(y0))))) MARK(cons1(2nd(2nd(cons(y0, y1))), z1)) -> c10(MARK(2nd(2nd(cons(y0, y1))))) MARK(cons1(2nd(2nd(s(y0))), z1)) -> c10(MARK(2nd(2nd(s(y0))))) MARK(cons1(2nd(2nd(cons1(y0, y1))), z1)) -> c10(MARK(2nd(2nd(cons1(y0, y1))))) MARK(cons1(2nd(2nd(y0)), z1)) -> c10(MARK(2nd(2nd(y0)))) MARK(cons1(2nd(from(y0)), z1)) -> c10(MARK(2nd(from(y0)))) MARK(cons1(2nd(from(2nd(y0))), z1)) -> c10(MARK(2nd(from(2nd(y0))))) MARK(cons1(2nd(from(from(y0))), z1)) -> c10(MARK(2nd(from(from(y0))))) MARK(cons1(2nd(from(cons(y0, y1))), z1)) -> c10(MARK(2nd(from(cons(y0, y1))))) MARK(cons1(2nd(from(s(y0))), z1)) -> c10(MARK(2nd(from(s(y0))))) MARK(cons1(2nd(from(cons1(y0, y1))), z1)) -> c10(MARK(2nd(from(cons1(y0, y1))))) MARK(cons1(2nd(cons1(y0, 2nd(y1))), z1)) -> c10(MARK(2nd(cons1(y0, 2nd(y1))))) MARK(cons1(2nd(cons1(y0, from(y1))), z1)) -> c10(MARK(2nd(cons1(y0, from(y1))))) MARK(cons1(2nd(cons1(y0, cons(y1, y2))), z1)) -> c10(MARK(2nd(cons1(y0, cons(y1, y2))))) MARK(cons1(2nd(cons1(2nd(y0), y1)), z1)) -> c10(MARK(2nd(cons1(2nd(y0), y1)))) MARK(cons1(2nd(cons1(from(y0), y1)), z1)) -> c10(MARK(2nd(cons1(from(y0), y1)))) MARK(cons1(2nd(cons1(cons(y0, y1), y2)), z1)) -> c10(MARK(2nd(cons1(cons(y0, y1), y2)))) MARK(cons1(2nd(cons1(s(y0), y1)), z1)) -> c10(MARK(2nd(cons1(s(y0), y1)))) MARK(cons1(2nd(cons1(cons1(y0, y1), y2)), z1)) -> c10(MARK(2nd(cons1(cons1(y0, y1), y2)))) MARK(cons1(2nd(cons1(y0, y1)), z1)) -> c10(MARK(2nd(cons1(y0, y1)))) MARK(cons1(2nd(cons1(y0, s(y1))), z1)) -> c10(MARK(2nd(cons1(y0, s(y1))))) MARK(cons1(2nd(cons1(y0, cons1(y1, y2))), z1)) -> c10(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(cons1(from(cons(y0, y1)), z1)) -> c10(MARK(from(cons(y0, y1)))) MARK(cons1(from(s(y0)), z1)) -> c10(MARK(from(s(y0)))) MARK(cons1(from(cons1(y0, y1)), z1)) -> c10(MARK(from(cons1(y0, y1)))) MARK(cons1(from(2nd(y0)), z1)) -> c10(MARK(from(2nd(y0)))) MARK(cons1(from(2nd(2nd(y0))), z1)) -> c10(MARK(from(2nd(2nd(y0))))) MARK(cons1(from(2nd(from(y0))), z1)) -> c10(MARK(from(2nd(from(y0))))) MARK(cons1(from(2nd(cons(y0, y1))), z1)) -> c10(MARK(from(2nd(cons(y0, y1))))) MARK(cons1(from(2nd(s(y0))), z1)) -> c10(MARK(from(2nd(s(y0))))) MARK(cons1(from(2nd(cons1(y0, y1))), z1)) -> c10(MARK(from(2nd(cons1(y0, y1))))) MARK(cons1(from(from(y0)), z1)) -> c10(MARK(from(from(y0)))) MARK(cons1(from(from(2nd(y0))), z1)) -> c10(MARK(from(from(2nd(y0))))) MARK(cons1(from(from(from(y0))), z1)) -> c10(MARK(from(from(from(y0))))) MARK(cons1(from(from(cons(y0, y1))), z1)) -> c10(MARK(from(from(cons(y0, y1))))) MARK(cons1(from(from(s(y0))), z1)) -> c10(MARK(from(from(s(y0))))) MARK(cons1(from(from(cons1(y0, y1))), z1)) -> c10(MARK(from(from(cons1(y0, y1))))) MARK(cons1(cons(cons(y0, y1), y2), z1)) -> c10(MARK(cons(cons(y0, y1), y2))) MARK(cons1(cons(s(y0), y1), z1)) -> c10(MARK(cons(s(y0), y1))) MARK(cons1(cons(cons1(y0, y1), y2), z1)) -> c10(MARK(cons(cons1(y0, y1), y2))) MARK(cons1(cons(2nd(cons(y0, y1)), y2), z1)) -> c10(MARK(cons(2nd(cons(y0, y1)), y2))) MARK(cons1(cons(2nd(s(y0)), y1), z1)) -> c10(MARK(cons(2nd(s(y0)), y1))) MARK(cons1(cons(2nd(2nd(2nd(y0))), y1), z1)) -> c10(MARK(cons(2nd(2nd(2nd(y0))), y1))) MARK(cons1(cons(2nd(2nd(from(y0))), y1), z1)) -> c10(MARK(cons(2nd(2nd(from(y0))), y1))) MARK(cons1(cons(2nd(2nd(cons(y0, y1))), y2), z1)) -> c10(MARK(cons(2nd(2nd(cons(y0, y1))), y2))) MARK(cons1(cons(2nd(2nd(s(y0))), y1), z1)) -> c10(MARK(cons(2nd(2nd(s(y0))), y1))) MARK(cons1(cons(2nd(2nd(cons1(y0, y1))), y2), z1)) -> c10(MARK(cons(2nd(2nd(cons1(y0, y1))), y2))) MARK(cons1(cons(2nd(2nd(y0)), y1), z1)) -> c10(MARK(cons(2nd(2nd(y0)), y1))) MARK(cons1(cons(2nd(from(y0)), y1), z1)) -> c10(MARK(cons(2nd(from(y0)), y1))) MARK(cons1(cons(2nd(from(2nd(y0))), y1), z1)) -> c10(MARK(cons(2nd(from(2nd(y0))), y1))) MARK(cons1(cons(2nd(from(from(y0))), y1), z1)) -> c10(MARK(cons(2nd(from(from(y0))), y1))) MARK(cons1(cons(2nd(from(cons(y0, y1))), y2), z1)) -> c10(MARK(cons(2nd(from(cons(y0, y1))), y2))) MARK(cons1(cons(2nd(from(s(y0))), y1), z1)) -> c10(MARK(cons(2nd(from(s(y0))), y1))) MARK(cons1(cons(2nd(from(cons1(y0, y1))), y2), z1)) -> c10(MARK(cons(2nd(from(cons1(y0, y1))), y2))) MARK(cons1(cons(2nd(cons1(y0, 2nd(y1))), y2), z1)) -> c10(MARK(cons(2nd(cons1(y0, 2nd(y1))), y2))) MARK(cons1(cons(2nd(cons1(y0, from(y1))), y2), z1)) -> c10(MARK(cons(2nd(cons1(y0, from(y1))), y2))) MARK(cons1(cons(2nd(cons1(y0, cons(y1, y2))), y3), z1)) -> c10(MARK(cons(2nd(cons1(y0, cons(y1, y2))), y3))) MARK(cons1(cons(2nd(cons1(2nd(y0), y1)), y2), z1)) -> c10(MARK(cons(2nd(cons1(2nd(y0), y1)), y2))) MARK(cons1(cons(2nd(cons1(from(y0), y1)), y2), z1)) -> c10(MARK(cons(2nd(cons1(from(y0), y1)), y2))) MARK(cons1(cons(2nd(cons1(cons(y0, y1), y2)), y3), z1)) -> c10(MARK(cons(2nd(cons1(cons(y0, y1), y2)), y3))) MARK(cons1(cons(2nd(cons1(s(y0), y1)), y2), z1)) -> c10(MARK(cons(2nd(cons1(s(y0), y1)), y2))) MARK(cons1(cons(2nd(cons1(cons1(y0, y1), y2)), y3), z1)) -> c10(MARK(cons(2nd(cons1(cons1(y0, y1), y2)), y3))) MARK(cons1(cons(2nd(cons1(y0, y1)), y2), z1)) -> c10(MARK(cons(2nd(cons1(y0, y1)), y2))) MARK(cons1(cons(2nd(cons1(y0, s(y1))), y2), z1)) -> c10(MARK(cons(2nd(cons1(y0, s(y1))), y2))) MARK(cons1(cons(2nd(cons1(y0, cons1(y1, y2))), y3), z1)) -> c10(MARK(cons(2nd(cons1(y0, cons1(y1, y2))), y3))) MARK(cons1(cons(from(cons(y0, y1)), y2), z1)) -> c10(MARK(cons(from(cons(y0, y1)), y2))) MARK(cons1(cons(from(s(y0)), y1), z1)) -> c10(MARK(cons(from(s(y0)), y1))) MARK(cons1(cons(from(cons1(y0, y1)), y2), z1)) -> c10(MARK(cons(from(cons1(y0, y1)), y2))) MARK(cons1(cons(from(2nd(y0)), y1), z1)) -> c10(MARK(cons(from(2nd(y0)), y1))) MARK(cons1(cons(from(2nd(2nd(y0))), y1), z1)) -> c10(MARK(cons(from(2nd(2nd(y0))), y1))) MARK(cons1(cons(from(2nd(from(y0))), y1), z1)) -> c10(MARK(cons(from(2nd(from(y0))), y1))) MARK(cons1(cons(from(2nd(cons(y0, y1))), y2), z1)) -> c10(MARK(cons(from(2nd(cons(y0, y1))), y2))) MARK(cons1(cons(from(2nd(s(y0))), y1), z1)) -> c10(MARK(cons(from(2nd(s(y0))), y1))) MARK(cons1(cons(from(2nd(cons1(y0, y1))), y2), z1)) -> c10(MARK(cons(from(2nd(cons1(y0, y1))), y2))) MARK(cons1(cons(from(from(y0)), y1), z1)) -> c10(MARK(cons(from(from(y0)), y1))) MARK(cons1(cons(from(from(2nd(y0))), y1), z1)) -> c10(MARK(cons(from(from(2nd(y0))), y1))) MARK(cons1(cons(from(from(from(y0))), y1), z1)) -> c10(MARK(cons(from(from(from(y0))), y1))) MARK(cons1(cons(from(from(cons(y0, y1))), y2), z1)) -> c10(MARK(cons(from(from(cons(y0, y1))), y2))) MARK(cons1(cons(from(from(s(y0))), y1), z1)) -> c10(MARK(cons(from(from(s(y0))), y1))) MARK(cons1(cons(from(from(cons1(y0, y1))), y2), z1)) -> c10(MARK(cons(from(from(cons1(y0, y1))), y2))) MARK(cons1(s(s(y0)), z1)) -> c10(MARK(s(s(y0)))) MARK(cons1(s(cons1(y0, y1)), z1)) -> c10(MARK(s(cons1(y0, y1)))) MARK(cons1(s(2nd(cons(y0, y1))), z1)) -> c10(MARK(s(2nd(cons(y0, y1))))) MARK(cons1(s(2nd(s(y0))), z1)) -> c10(MARK(s(2nd(s(y0))))) MARK(cons1(s(2nd(2nd(2nd(y0)))), z1)) -> c10(MARK(s(2nd(2nd(2nd(y0)))))) MARK(cons1(s(2nd(2nd(from(y0)))), z1)) -> c10(MARK(s(2nd(2nd(from(y0)))))) MARK(cons1(s(2nd(2nd(cons(y0, y1)))), z1)) -> c10(MARK(s(2nd(2nd(cons(y0, y1)))))) MARK(cons1(s(2nd(2nd(s(y0)))), z1)) -> c10(MARK(s(2nd(2nd(s(y0)))))) MARK(cons1(s(2nd(2nd(cons1(y0, y1)))), z1)) -> c10(MARK(s(2nd(2nd(cons1(y0, y1)))))) MARK(cons1(s(2nd(2nd(y0))), z1)) -> c10(MARK(s(2nd(2nd(y0))))) MARK(cons1(s(2nd(from(y0))), z1)) -> c10(MARK(s(2nd(from(y0))))) MARK(cons1(s(2nd(from(2nd(y0)))), z1)) -> c10(MARK(s(2nd(from(2nd(y0)))))) MARK(cons1(s(2nd(from(from(y0)))), z1)) -> c10(MARK(s(2nd(from(from(y0)))))) MARK(cons1(s(2nd(from(cons(y0, y1)))), z1)) -> c10(MARK(s(2nd(from(cons(y0, y1)))))) MARK(cons1(s(2nd(from(s(y0)))), z1)) -> c10(MARK(s(2nd(from(s(y0)))))) MARK(cons1(s(2nd(from(cons1(y0, y1)))), z1)) -> c10(MARK(s(2nd(from(cons1(y0, y1)))))) MARK(cons1(s(2nd(cons1(y0, 2nd(y1)))), z1)) -> c10(MARK(s(2nd(cons1(y0, 2nd(y1)))))) MARK(cons1(s(2nd(cons1(y0, from(y1)))), z1)) -> c10(MARK(s(2nd(cons1(y0, from(y1)))))) MARK(cons1(s(2nd(cons1(y0, cons(y1, y2)))), z1)) -> c10(MARK(s(2nd(cons1(y0, cons(y1, y2)))))) MARK(cons1(s(2nd(cons1(2nd(y0), y1))), z1)) -> c10(MARK(s(2nd(cons1(2nd(y0), y1))))) MARK(cons1(s(2nd(cons1(from(y0), y1))), z1)) -> c10(MARK(s(2nd(cons1(from(y0), y1))))) MARK(cons1(s(2nd(cons1(cons(y0, y1), y2))), z1)) -> c10(MARK(s(2nd(cons1(cons(y0, y1), y2))))) MARK(cons1(s(2nd(cons1(s(y0), y1))), z1)) -> c10(MARK(s(2nd(cons1(s(y0), y1))))) MARK(cons1(s(2nd(cons1(cons1(y0, y1), y2))), z1)) -> c10(MARK(s(2nd(cons1(cons1(y0, y1), y2))))) MARK(cons1(s(2nd(cons1(y0, y1))), z1)) -> c10(MARK(s(2nd(cons1(y0, y1))))) MARK(cons1(s(2nd(cons1(y0, s(y1)))), z1)) -> c10(MARK(s(2nd(cons1(y0, s(y1)))))) MARK(cons1(s(2nd(cons1(y0, cons1(y1, y2)))), z1)) -> c10(MARK(s(2nd(cons1(y0, cons1(y1, y2)))))) MARK(cons1(s(from(cons(y0, y1))), z1)) -> c10(MARK(s(from(cons(y0, y1))))) MARK(cons1(s(from(s(y0))), z1)) -> c10(MARK(s(from(s(y0))))) MARK(cons1(s(from(cons1(y0, y1))), z1)) -> c10(MARK(s(from(cons1(y0, y1))))) MARK(cons1(s(from(2nd(y0))), z1)) -> c10(MARK(s(from(2nd(y0))))) MARK(cons1(s(from(2nd(2nd(y0)))), z1)) -> c10(MARK(s(from(2nd(2nd(y0)))))) MARK(cons1(s(from(2nd(from(y0)))), z1)) -> c10(MARK(s(from(2nd(from(y0)))))) MARK(cons1(s(from(2nd(cons(y0, y1)))), z1)) -> c10(MARK(s(from(2nd(cons(y0, y1)))))) MARK(cons1(s(from(2nd(s(y0)))), z1)) -> c10(MARK(s(from(2nd(s(y0)))))) MARK(cons1(s(from(2nd(cons1(y0, y1)))), z1)) -> c10(MARK(s(from(2nd(cons1(y0, y1)))))) MARK(cons1(s(from(from(y0))), z1)) -> c10(MARK(s(from(from(y0))))) MARK(cons1(s(from(from(2nd(y0)))), z1)) -> c10(MARK(s(from(from(2nd(y0)))))) MARK(cons1(s(from(from(from(y0)))), z1)) -> c10(MARK(s(from(from(from(y0)))))) MARK(cons1(s(from(from(cons(y0, y1)))), z1)) -> c10(MARK(s(from(from(cons(y0, y1)))))) MARK(cons1(s(from(from(s(y0)))), z1)) -> c10(MARK(s(from(from(s(y0)))))) MARK(cons1(s(from(from(cons1(y0, y1)))), z1)) -> c10(MARK(s(from(from(cons1(y0, y1)))))) MARK(cons1(s(cons(cons(y0, y1), y2)), z1)) -> c10(MARK(s(cons(cons(y0, y1), y2)))) MARK(cons1(s(cons(s(y0), y1)), z1)) -> c10(MARK(s(cons(s(y0), y1)))) MARK(cons1(s(cons(cons1(y0, y1), y2)), z1)) -> c10(MARK(s(cons(cons1(y0, y1), y2)))) MARK(cons1(s(cons(2nd(cons(y0, y1)), y2)), z1)) -> c10(MARK(s(cons(2nd(cons(y0, y1)), y2)))) MARK(cons1(s(cons(2nd(s(y0)), y1)), z1)) -> c10(MARK(s(cons(2nd(s(y0)), y1)))) MARK(cons1(s(cons(2nd(2nd(2nd(y0))), y1)), z1)) -> c10(MARK(s(cons(2nd(2nd(2nd(y0))), y1)))) MARK(cons1(s(cons(2nd(2nd(from(y0))), y1)), z1)) -> c10(MARK(s(cons(2nd(2nd(from(y0))), y1)))) MARK(cons1(s(cons(2nd(2nd(cons(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(2nd(cons(y0, y1))), y2)))) MARK(cons1(s(cons(2nd(2nd(s(y0))), y1)), z1)) -> c10(MARK(s(cons(2nd(2nd(s(y0))), y1)))) MARK(cons1(s(cons(2nd(2nd(cons1(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(2nd(cons1(y0, y1))), y2)))) MARK(cons1(s(cons(2nd(2nd(y0)), y1)), z1)) -> c10(MARK(s(cons(2nd(2nd(y0)), y1)))) MARK(cons1(s(cons(2nd(from(y0)), y1)), z1)) -> c10(MARK(s(cons(2nd(from(y0)), y1)))) MARK(cons1(s(cons(2nd(from(2nd(y0))), y1)), z1)) -> c10(MARK(s(cons(2nd(from(2nd(y0))), y1)))) MARK(cons1(s(cons(2nd(from(from(y0))), y1)), z1)) -> c10(MARK(s(cons(2nd(from(from(y0))), y1)))) MARK(cons1(s(cons(2nd(from(cons(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(from(cons(y0, y1))), y2)))) MARK(cons1(s(cons(2nd(from(s(y0))), y1)), z1)) -> c10(MARK(s(cons(2nd(from(s(y0))), y1)))) MARK(cons1(s(cons(2nd(from(cons1(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(from(cons1(y0, y1))), y2)))) MARK(cons1(s(cons(2nd(cons1(y0, 2nd(y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(cons1(y0, 2nd(y1))), y2)))) MARK(cons1(s(cons(2nd(cons1(y0, from(y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(cons1(y0, from(y1))), y2)))) MARK(cons1(s(cons(2nd(cons1(y0, cons(y1, y2))), y3)), z1)) -> c10(MARK(s(cons(2nd(cons1(y0, cons(y1, y2))), y3)))) MARK(cons1(s(cons(2nd(cons1(2nd(y0), y1)), y2)), z1)) -> c10(MARK(s(cons(2nd(cons1(2nd(y0), y1)), y2)))) MARK(cons1(s(cons(2nd(cons1(from(y0), y1)), y2)), z1)) -> c10(MARK(s(cons(2nd(cons1(from(y0), y1)), y2)))) MARK(cons1(s(cons(2nd(cons1(cons(y0, y1), y2)), y3)), z1)) -> c10(MARK(s(cons(2nd(cons1(cons(y0, y1), y2)), y3)))) MARK(cons1(s(cons(2nd(cons1(s(y0), y1)), y2)), z1)) -> c10(MARK(s(cons(2nd(cons1(s(y0), y1)), y2)))) MARK(cons1(s(cons(2nd(cons1(cons1(y0, y1), y2)), y3)), z1)) -> c10(MARK(s(cons(2nd(cons1(cons1(y0, y1), y2)), y3)))) MARK(cons1(s(cons(2nd(cons1(y0, y1)), y2)), z1)) -> c10(MARK(s(cons(2nd(cons1(y0, y1)), y2)))) MARK(cons1(s(cons(2nd(cons1(y0, s(y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(cons1(y0, s(y1))), y2)))) MARK(cons1(s(cons(2nd(cons1(y0, cons1(y1, y2))), y3)), z1)) -> c10(MARK(s(cons(2nd(cons1(y0, cons1(y1, y2))), y3)))) MARK(cons1(s(cons(from(cons(y0, y1)), y2)), z1)) -> c10(MARK(s(cons(from(cons(y0, y1)), y2)))) MARK(cons1(s(cons(from(s(y0)), y1)), z1)) -> c10(MARK(s(cons(from(s(y0)), y1)))) MARK(cons1(s(cons(from(cons1(y0, y1)), y2)), z1)) -> c10(MARK(s(cons(from(cons1(y0, y1)), y2)))) MARK(cons1(s(cons(from(2nd(y0)), y1)), z1)) -> c10(MARK(s(cons(from(2nd(y0)), y1)))) MARK(cons1(s(cons(from(2nd(2nd(y0))), y1)), z1)) -> c10(MARK(s(cons(from(2nd(2nd(y0))), y1)))) MARK(cons1(s(cons(from(2nd(from(y0))), y1)), z1)) -> c10(MARK(s(cons(from(2nd(from(y0))), y1)))) MARK(cons1(s(cons(from(2nd(cons(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(from(2nd(cons(y0, y1))), y2)))) MARK(cons1(s(cons(from(2nd(s(y0))), y1)), z1)) -> c10(MARK(s(cons(from(2nd(s(y0))), y1)))) MARK(cons1(s(cons(from(2nd(cons1(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(from(2nd(cons1(y0, y1))), y2)))) MARK(cons1(s(cons(from(from(y0)), y1)), z1)) -> c10(MARK(s(cons(from(from(y0)), y1)))) MARK(cons1(s(cons(from(from(2nd(y0))), y1)), z1)) -> c10(MARK(s(cons(from(from(2nd(y0))), y1)))) MARK(cons1(s(cons(from(from(from(y0))), y1)), z1)) -> c10(MARK(s(cons(from(from(from(y0))), y1)))) MARK(cons1(s(cons(from(from(cons(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(from(from(cons(y0, y1))), y2)))) MARK(cons1(s(cons(from(from(s(y0))), y1)), z1)) -> c10(MARK(s(cons(from(from(s(y0))), y1)))) MARK(cons1(s(cons(from(from(cons1(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(from(from(cons1(y0, y1))), y2)))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: MARK_1, A__2ND_1, A__FROM_1 Compound Symbols: c11_1, c1_1, c2_1, c6_2, c6_1, c1_2, c2_2, c_1, c4_1, c7_2, c8_1, c9_1, c10_1 ---------------------------------------- (125) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(cons1(z0, z1)) -> c11(MARK(z1)) by MARK(cons1(z0, cons1(y0, y1))) -> c11(MARK(cons1(y0, y1))) MARK(cons1(z0, 2nd(cons(y0, y1)))) -> c11(MARK(2nd(cons(y0, y1)))) MARK(cons1(z0, 2nd(s(y0)))) -> c11(MARK(2nd(s(y0)))) MARK(cons1(z0, 2nd(2nd(2nd(y0))))) -> c11(MARK(2nd(2nd(2nd(y0))))) MARK(cons1(z0, 2nd(2nd(from(y0))))) -> c11(MARK(2nd(2nd(from(y0))))) MARK(cons1(z0, 2nd(2nd(cons(y0, y1))))) -> c11(MARK(2nd(2nd(cons(y0, y1))))) MARK(cons1(z0, 2nd(2nd(s(y0))))) -> c11(MARK(2nd(2nd(s(y0))))) MARK(cons1(z0, 2nd(2nd(cons1(y0, y1))))) -> c11(MARK(2nd(2nd(cons1(y0, y1))))) MARK(cons1(z0, 2nd(2nd(y0)))) -> c11(MARK(2nd(2nd(y0)))) MARK(cons1(z0, 2nd(from(y0)))) -> c11(MARK(2nd(from(y0)))) MARK(cons1(z0, 2nd(from(2nd(y0))))) -> c11(MARK(2nd(from(2nd(y0))))) MARK(cons1(z0, 2nd(from(from(y0))))) -> c11(MARK(2nd(from(from(y0))))) MARK(cons1(z0, 2nd(from(cons(y0, y1))))) -> c11(MARK(2nd(from(cons(y0, y1))))) MARK(cons1(z0, 2nd(from(s(y0))))) -> c11(MARK(2nd(from(s(y0))))) MARK(cons1(z0, 2nd(from(cons1(y0, y1))))) -> c11(MARK(2nd(from(cons1(y0, y1))))) MARK(cons1(z0, 2nd(cons1(y0, 2nd(y1))))) -> c11(MARK(2nd(cons1(y0, 2nd(y1))))) MARK(cons1(z0, 2nd(cons1(y0, from(y1))))) -> c11(MARK(2nd(cons1(y0, from(y1))))) MARK(cons1(z0, 2nd(cons1(y0, cons(y1, y2))))) -> c11(MARK(2nd(cons1(y0, cons(y1, y2))))) MARK(cons1(z0, 2nd(cons1(2nd(y0), y1)))) -> c11(MARK(2nd(cons1(2nd(y0), y1)))) MARK(cons1(z0, 2nd(cons1(from(y0), y1)))) -> c11(MARK(2nd(cons1(from(y0), y1)))) MARK(cons1(z0, 2nd(cons1(cons(y0, y1), y2)))) -> c11(MARK(2nd(cons1(cons(y0, y1), y2)))) MARK(cons1(z0, 2nd(cons1(s(y0), y1)))) -> c11(MARK(2nd(cons1(s(y0), y1)))) MARK(cons1(z0, 2nd(cons1(cons1(y0, y1), y2)))) -> c11(MARK(2nd(cons1(cons1(y0, y1), y2)))) MARK(cons1(z0, 2nd(cons1(y0, y1)))) -> c11(MARK(2nd(cons1(y0, y1)))) MARK(cons1(z0, 2nd(cons1(y0, s(y1))))) -> c11(MARK(2nd(cons1(y0, s(y1))))) MARK(cons1(z0, 2nd(cons1(y0, cons1(y1, y2))))) -> c11(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(cons1(z0, from(cons(y0, y1)))) -> c11(MARK(from(cons(y0, y1)))) MARK(cons1(z0, from(s(y0)))) -> c11(MARK(from(s(y0)))) MARK(cons1(z0, from(cons1(y0, y1)))) -> c11(MARK(from(cons1(y0, y1)))) MARK(cons1(z0, from(2nd(y0)))) -> c11(MARK(from(2nd(y0)))) MARK(cons1(z0, from(2nd(2nd(y0))))) -> c11(MARK(from(2nd(2nd(y0))))) MARK(cons1(z0, from(2nd(from(y0))))) -> c11(MARK(from(2nd(from(y0))))) MARK(cons1(z0, from(2nd(cons(y0, y1))))) -> c11(MARK(from(2nd(cons(y0, y1))))) MARK(cons1(z0, from(2nd(s(y0))))) -> c11(MARK(from(2nd(s(y0))))) MARK(cons1(z0, from(2nd(cons1(y0, y1))))) -> c11(MARK(from(2nd(cons1(y0, y1))))) MARK(cons1(z0, from(from(y0)))) -> c11(MARK(from(from(y0)))) MARK(cons1(z0, from(from(2nd(y0))))) -> c11(MARK(from(from(2nd(y0))))) MARK(cons1(z0, from(from(from(y0))))) -> c11(MARK(from(from(from(y0))))) MARK(cons1(z0, from(from(cons(y0, y1))))) -> c11(MARK(from(from(cons(y0, y1))))) MARK(cons1(z0, from(from(s(y0))))) -> c11(MARK(from(from(s(y0))))) MARK(cons1(z0, from(from(cons1(y0, y1))))) -> c11(MARK(from(from(cons1(y0, y1))))) MARK(cons1(z0, cons(cons(y0, y1), y2))) -> c11(MARK(cons(cons(y0, y1), y2))) MARK(cons1(z0, cons(s(y0), y1))) -> c11(MARK(cons(s(y0), y1))) MARK(cons1(z0, cons(cons1(y0, y1), y2))) -> c11(MARK(cons(cons1(y0, y1), y2))) MARK(cons1(z0, cons(2nd(cons(y0, y1)), y2))) -> c11(MARK(cons(2nd(cons(y0, y1)), y2))) MARK(cons1(z0, cons(2nd(s(y0)), y1))) -> c11(MARK(cons(2nd(s(y0)), y1))) MARK(cons1(z0, cons(2nd(2nd(2nd(y0))), y1))) -> c11(MARK(cons(2nd(2nd(2nd(y0))), y1))) MARK(cons1(z0, cons(2nd(2nd(from(y0))), y1))) -> c11(MARK(cons(2nd(2nd(from(y0))), y1))) MARK(cons1(z0, cons(2nd(2nd(cons(y0, y1))), y2))) -> c11(MARK(cons(2nd(2nd(cons(y0, y1))), y2))) MARK(cons1(z0, cons(2nd(2nd(s(y0))), y1))) -> c11(MARK(cons(2nd(2nd(s(y0))), y1))) MARK(cons1(z0, cons(2nd(2nd(cons1(y0, y1))), y2))) -> c11(MARK(cons(2nd(2nd(cons1(y0, y1))), y2))) MARK(cons1(z0, cons(2nd(2nd(y0)), y1))) -> c11(MARK(cons(2nd(2nd(y0)), y1))) MARK(cons1(z0, cons(2nd(from(y0)), y1))) -> c11(MARK(cons(2nd(from(y0)), y1))) MARK(cons1(z0, cons(2nd(from(2nd(y0))), y1))) -> c11(MARK(cons(2nd(from(2nd(y0))), y1))) MARK(cons1(z0, cons(2nd(from(from(y0))), y1))) -> c11(MARK(cons(2nd(from(from(y0))), y1))) MARK(cons1(z0, cons(2nd(from(cons(y0, y1))), y2))) -> c11(MARK(cons(2nd(from(cons(y0, y1))), y2))) MARK(cons1(z0, cons(2nd(from(s(y0))), y1))) -> c11(MARK(cons(2nd(from(s(y0))), y1))) MARK(cons1(z0, cons(2nd(from(cons1(y0, y1))), y2))) -> c11(MARK(cons(2nd(from(cons1(y0, y1))), y2))) MARK(cons1(z0, cons(2nd(cons1(y0, 2nd(y1))), y2))) -> c11(MARK(cons(2nd(cons1(y0, 2nd(y1))), y2))) MARK(cons1(z0, cons(2nd(cons1(y0, from(y1))), y2))) -> c11(MARK(cons(2nd(cons1(y0, from(y1))), y2))) MARK(cons1(z0, cons(2nd(cons1(y0, cons(y1, y2))), y3))) -> c11(MARK(cons(2nd(cons1(y0, cons(y1, y2))), y3))) MARK(cons1(z0, cons(2nd(cons1(2nd(y0), y1)), y2))) -> c11(MARK(cons(2nd(cons1(2nd(y0), y1)), y2))) MARK(cons1(z0, cons(2nd(cons1(from(y0), y1)), y2))) -> c11(MARK(cons(2nd(cons1(from(y0), y1)), y2))) MARK(cons1(z0, cons(2nd(cons1(cons(y0, y1), y2)), y3))) -> c11(MARK(cons(2nd(cons1(cons(y0, y1), y2)), y3))) MARK(cons1(z0, cons(2nd(cons1(s(y0), y1)), y2))) -> c11(MARK(cons(2nd(cons1(s(y0), y1)), y2))) MARK(cons1(z0, cons(2nd(cons1(cons1(y0, y1), y2)), y3))) -> c11(MARK(cons(2nd(cons1(cons1(y0, y1), y2)), y3))) MARK(cons1(z0, cons(2nd(cons1(y0, y1)), y2))) -> c11(MARK(cons(2nd(cons1(y0, y1)), y2))) MARK(cons1(z0, cons(2nd(cons1(y0, s(y1))), y2))) -> c11(MARK(cons(2nd(cons1(y0, s(y1))), y2))) MARK(cons1(z0, cons(2nd(cons1(y0, cons1(y1, y2))), y3))) -> c11(MARK(cons(2nd(cons1(y0, cons1(y1, y2))), y3))) MARK(cons1(z0, cons(from(cons(y0, y1)), y2))) -> c11(MARK(cons(from(cons(y0, y1)), y2))) MARK(cons1(z0, cons(from(s(y0)), y1))) -> c11(MARK(cons(from(s(y0)), y1))) MARK(cons1(z0, cons(from(cons1(y0, y1)), y2))) -> c11(MARK(cons(from(cons1(y0, y1)), y2))) MARK(cons1(z0, cons(from(2nd(y0)), y1))) -> c11(MARK(cons(from(2nd(y0)), y1))) MARK(cons1(z0, cons(from(2nd(2nd(y0))), y1))) -> c11(MARK(cons(from(2nd(2nd(y0))), y1))) MARK(cons1(z0, cons(from(2nd(from(y0))), y1))) -> c11(MARK(cons(from(2nd(from(y0))), y1))) MARK(cons1(z0, cons(from(2nd(cons(y0, y1))), y2))) -> c11(MARK(cons(from(2nd(cons(y0, y1))), y2))) MARK(cons1(z0, cons(from(2nd(s(y0))), y1))) -> c11(MARK(cons(from(2nd(s(y0))), y1))) MARK(cons1(z0, cons(from(2nd(cons1(y0, y1))), y2))) -> c11(MARK(cons(from(2nd(cons1(y0, y1))), y2))) MARK(cons1(z0, cons(from(from(y0)), y1))) -> c11(MARK(cons(from(from(y0)), y1))) MARK(cons1(z0, cons(from(from(2nd(y0))), y1))) -> c11(MARK(cons(from(from(2nd(y0))), y1))) MARK(cons1(z0, cons(from(from(from(y0))), y1))) -> c11(MARK(cons(from(from(from(y0))), y1))) MARK(cons1(z0, cons(from(from(cons(y0, y1))), y2))) -> c11(MARK(cons(from(from(cons(y0, y1))), y2))) MARK(cons1(z0, cons(from(from(s(y0))), y1))) -> c11(MARK(cons(from(from(s(y0))), y1))) MARK(cons1(z0, cons(from(from(cons1(y0, y1))), y2))) -> c11(MARK(cons(from(from(cons1(y0, y1))), y2))) MARK(cons1(z0, s(s(y0)))) -> c11(MARK(s(s(y0)))) MARK(cons1(z0, s(cons1(y0, y1)))) -> c11(MARK(s(cons1(y0, y1)))) MARK(cons1(z0, s(2nd(cons(y0, y1))))) -> c11(MARK(s(2nd(cons(y0, y1))))) MARK(cons1(z0, s(2nd(s(y0))))) -> c11(MARK(s(2nd(s(y0))))) MARK(cons1(z0, s(2nd(2nd(2nd(y0)))))) -> c11(MARK(s(2nd(2nd(2nd(y0)))))) MARK(cons1(z0, s(2nd(2nd(from(y0)))))) -> c11(MARK(s(2nd(2nd(from(y0)))))) MARK(cons1(z0, s(2nd(2nd(cons(y0, y1)))))) -> c11(MARK(s(2nd(2nd(cons(y0, y1)))))) MARK(cons1(z0, s(2nd(2nd(s(y0)))))) -> c11(MARK(s(2nd(2nd(s(y0)))))) MARK(cons1(z0, s(2nd(2nd(cons1(y0, y1)))))) -> c11(MARK(s(2nd(2nd(cons1(y0, y1)))))) MARK(cons1(z0, s(2nd(2nd(y0))))) -> c11(MARK(s(2nd(2nd(y0))))) MARK(cons1(z0, s(2nd(from(y0))))) -> c11(MARK(s(2nd(from(y0))))) MARK(cons1(z0, s(2nd(from(2nd(y0)))))) -> c11(MARK(s(2nd(from(2nd(y0)))))) MARK(cons1(z0, s(2nd(from(from(y0)))))) -> c11(MARK(s(2nd(from(from(y0)))))) MARK(cons1(z0, s(2nd(from(cons(y0, y1)))))) -> c11(MARK(s(2nd(from(cons(y0, y1)))))) MARK(cons1(z0, s(2nd(from(s(y0)))))) -> c11(MARK(s(2nd(from(s(y0)))))) MARK(cons1(z0, s(2nd(from(cons1(y0, y1)))))) -> c11(MARK(s(2nd(from(cons1(y0, y1)))))) MARK(cons1(z0, s(2nd(cons1(y0, 2nd(y1)))))) -> c11(MARK(s(2nd(cons1(y0, 2nd(y1)))))) MARK(cons1(z0, s(2nd(cons1(y0, from(y1)))))) -> c11(MARK(s(2nd(cons1(y0, from(y1)))))) MARK(cons1(z0, s(2nd(cons1(y0, cons(y1, y2)))))) -> c11(MARK(s(2nd(cons1(y0, cons(y1, y2)))))) MARK(cons1(z0, s(2nd(cons1(2nd(y0), y1))))) -> c11(MARK(s(2nd(cons1(2nd(y0), y1))))) MARK(cons1(z0, s(2nd(cons1(from(y0), y1))))) -> c11(MARK(s(2nd(cons1(from(y0), y1))))) MARK(cons1(z0, s(2nd(cons1(cons(y0, y1), y2))))) -> c11(MARK(s(2nd(cons1(cons(y0, y1), y2))))) MARK(cons1(z0, s(2nd(cons1(s(y0), y1))))) -> c11(MARK(s(2nd(cons1(s(y0), y1))))) MARK(cons1(z0, s(2nd(cons1(cons1(y0, y1), y2))))) -> c11(MARK(s(2nd(cons1(cons1(y0, y1), y2))))) MARK(cons1(z0, s(2nd(cons1(y0, y1))))) -> c11(MARK(s(2nd(cons1(y0, y1))))) MARK(cons1(z0, s(2nd(cons1(y0, s(y1)))))) -> c11(MARK(s(2nd(cons1(y0, s(y1)))))) MARK(cons1(z0, s(2nd(cons1(y0, cons1(y1, y2)))))) -> c11(MARK(s(2nd(cons1(y0, cons1(y1, y2)))))) MARK(cons1(z0, s(from(cons(y0, y1))))) -> c11(MARK(s(from(cons(y0, y1))))) MARK(cons1(z0, s(from(s(y0))))) -> c11(MARK(s(from(s(y0))))) MARK(cons1(z0, s(from(cons1(y0, y1))))) -> c11(MARK(s(from(cons1(y0, y1))))) MARK(cons1(z0, s(from(2nd(y0))))) -> c11(MARK(s(from(2nd(y0))))) MARK(cons1(z0, s(from(2nd(2nd(y0)))))) -> c11(MARK(s(from(2nd(2nd(y0)))))) MARK(cons1(z0, s(from(2nd(from(y0)))))) -> c11(MARK(s(from(2nd(from(y0)))))) MARK(cons1(z0, s(from(2nd(cons(y0, y1)))))) -> c11(MARK(s(from(2nd(cons(y0, y1)))))) MARK(cons1(z0, s(from(2nd(s(y0)))))) -> c11(MARK(s(from(2nd(s(y0)))))) MARK(cons1(z0, s(from(2nd(cons1(y0, y1)))))) -> c11(MARK(s(from(2nd(cons1(y0, y1)))))) MARK(cons1(z0, s(from(from(y0))))) -> c11(MARK(s(from(from(y0))))) MARK(cons1(z0, s(from(from(2nd(y0)))))) -> c11(MARK(s(from(from(2nd(y0)))))) MARK(cons1(z0, s(from(from(from(y0)))))) -> c11(MARK(s(from(from(from(y0)))))) MARK(cons1(z0, s(from(from(cons(y0, y1)))))) -> c11(MARK(s(from(from(cons(y0, y1)))))) MARK(cons1(z0, s(from(from(s(y0)))))) -> c11(MARK(s(from(from(s(y0)))))) MARK(cons1(z0, s(from(from(cons1(y0, y1)))))) -> c11(MARK(s(from(from(cons1(y0, y1)))))) MARK(cons1(z0, s(cons(cons(y0, y1), y2)))) -> c11(MARK(s(cons(cons(y0, y1), y2)))) MARK(cons1(z0, s(cons(s(y0), y1)))) -> c11(MARK(s(cons(s(y0), y1)))) MARK(cons1(z0, s(cons(cons1(y0, y1), y2)))) -> c11(MARK(s(cons(cons1(y0, y1), y2)))) MARK(cons1(z0, s(cons(2nd(cons(y0, y1)), y2)))) -> c11(MARK(s(cons(2nd(cons(y0, y1)), y2)))) MARK(cons1(z0, s(cons(2nd(s(y0)), y1)))) -> c11(MARK(s(cons(2nd(s(y0)), y1)))) MARK(cons1(z0, s(cons(2nd(2nd(2nd(y0))), y1)))) -> c11(MARK(s(cons(2nd(2nd(2nd(y0))), y1)))) MARK(cons1(z0, s(cons(2nd(2nd(from(y0))), y1)))) -> c11(MARK(s(cons(2nd(2nd(from(y0))), y1)))) MARK(cons1(z0, s(cons(2nd(2nd(cons(y0, y1))), y2)))) -> c11(MARK(s(cons(2nd(2nd(cons(y0, y1))), y2)))) MARK(cons1(z0, s(cons(2nd(2nd(s(y0))), y1)))) -> c11(MARK(s(cons(2nd(2nd(s(y0))), y1)))) MARK(cons1(z0, s(cons(2nd(2nd(cons1(y0, y1))), y2)))) -> c11(MARK(s(cons(2nd(2nd(cons1(y0, y1))), y2)))) MARK(cons1(z0, s(cons(2nd(2nd(y0)), y1)))) -> c11(MARK(s(cons(2nd(2nd(y0)), y1)))) MARK(cons1(z0, s(cons(2nd(from(y0)), y1)))) -> c11(MARK(s(cons(2nd(from(y0)), y1)))) MARK(cons1(z0, s(cons(2nd(from(2nd(y0))), y1)))) -> c11(MARK(s(cons(2nd(from(2nd(y0))), y1)))) MARK(cons1(z0, s(cons(2nd(from(from(y0))), y1)))) -> c11(MARK(s(cons(2nd(from(from(y0))), y1)))) MARK(cons1(z0, s(cons(2nd(from(cons(y0, y1))), y2)))) -> c11(MARK(s(cons(2nd(from(cons(y0, y1))), y2)))) MARK(cons1(z0, s(cons(2nd(from(s(y0))), y1)))) -> c11(MARK(s(cons(2nd(from(s(y0))), y1)))) MARK(cons1(z0, s(cons(2nd(from(cons1(y0, y1))), y2)))) -> c11(MARK(s(cons(2nd(from(cons1(y0, y1))), y2)))) MARK(cons1(z0, s(cons(2nd(cons1(y0, 2nd(y1))), y2)))) -> c11(MARK(s(cons(2nd(cons1(y0, 2nd(y1))), y2)))) MARK(cons1(z0, s(cons(2nd(cons1(y0, from(y1))), y2)))) -> c11(MARK(s(cons(2nd(cons1(y0, from(y1))), y2)))) MARK(cons1(z0, s(cons(2nd(cons1(y0, cons(y1, y2))), y3)))) -> c11(MARK(s(cons(2nd(cons1(y0, cons(y1, y2))), y3)))) MARK(cons1(z0, s(cons(2nd(cons1(2nd(y0), y1)), y2)))) -> c11(MARK(s(cons(2nd(cons1(2nd(y0), y1)), y2)))) MARK(cons1(z0, s(cons(2nd(cons1(from(y0), y1)), y2)))) -> c11(MARK(s(cons(2nd(cons1(from(y0), y1)), y2)))) MARK(cons1(z0, s(cons(2nd(cons1(cons(y0, y1), y2)), y3)))) -> c11(MARK(s(cons(2nd(cons1(cons(y0, y1), y2)), y3)))) MARK(cons1(z0, s(cons(2nd(cons1(s(y0), y1)), y2)))) -> c11(MARK(s(cons(2nd(cons1(s(y0), y1)), y2)))) MARK(cons1(z0, s(cons(2nd(cons1(cons1(y0, y1), y2)), y3)))) -> c11(MARK(s(cons(2nd(cons1(cons1(y0, y1), y2)), y3)))) MARK(cons1(z0, s(cons(2nd(cons1(y0, y1)), y2)))) -> c11(MARK(s(cons(2nd(cons1(y0, y1)), y2)))) MARK(cons1(z0, s(cons(2nd(cons1(y0, s(y1))), y2)))) -> c11(MARK(s(cons(2nd(cons1(y0, s(y1))), y2)))) MARK(cons1(z0, s(cons(2nd(cons1(y0, cons1(y1, y2))), y3)))) -> c11(MARK(s(cons(2nd(cons1(y0, cons1(y1, y2))), y3)))) MARK(cons1(z0, s(cons(from(cons(y0, y1)), y2)))) -> c11(MARK(s(cons(from(cons(y0, y1)), y2)))) MARK(cons1(z0, s(cons(from(s(y0)), y1)))) -> c11(MARK(s(cons(from(s(y0)), y1)))) MARK(cons1(z0, s(cons(from(cons1(y0, y1)), y2)))) -> c11(MARK(s(cons(from(cons1(y0, y1)), y2)))) MARK(cons1(z0, s(cons(from(2nd(y0)), y1)))) -> c11(MARK(s(cons(from(2nd(y0)), y1)))) MARK(cons1(z0, s(cons(from(2nd(2nd(y0))), y1)))) -> c11(MARK(s(cons(from(2nd(2nd(y0))), y1)))) MARK(cons1(z0, s(cons(from(2nd(from(y0))), y1)))) -> c11(MARK(s(cons(from(2nd(from(y0))), y1)))) MARK(cons1(z0, s(cons(from(2nd(cons(y0, y1))), y2)))) -> c11(MARK(s(cons(from(2nd(cons(y0, y1))), y2)))) MARK(cons1(z0, s(cons(from(2nd(s(y0))), y1)))) -> c11(MARK(s(cons(from(2nd(s(y0))), y1)))) MARK(cons1(z0, s(cons(from(2nd(cons1(y0, y1))), y2)))) -> c11(MARK(s(cons(from(2nd(cons1(y0, y1))), y2)))) MARK(cons1(z0, s(cons(from(from(y0)), y1)))) -> c11(MARK(s(cons(from(from(y0)), y1)))) MARK(cons1(z0, s(cons(from(from(2nd(y0))), y1)))) -> c11(MARK(s(cons(from(from(2nd(y0))), y1)))) MARK(cons1(z0, s(cons(from(from(from(y0))), y1)))) -> c11(MARK(s(cons(from(from(from(y0))), y1)))) MARK(cons1(z0, s(cons(from(from(cons(y0, y1))), y2)))) -> c11(MARK(s(cons(from(from(cons(y0, y1))), y2)))) MARK(cons1(z0, s(cons(from(from(s(y0))), y1)))) -> c11(MARK(s(cons(from(from(s(y0))), y1)))) MARK(cons1(z0, s(cons(from(from(cons1(y0, y1))), y2)))) -> c11(MARK(s(cons(from(from(cons1(y0, y1))), y2)))) MARK(cons1(z0, cons1(cons1(y0, y1), y2))) -> c11(MARK(cons1(cons1(y0, y1), y2))) MARK(cons1(z0, cons1(2nd(cons(y0, y1)), y2))) -> c11(MARK(cons1(2nd(cons(y0, y1)), y2))) MARK(cons1(z0, cons1(2nd(s(y0)), y1))) -> c11(MARK(cons1(2nd(s(y0)), y1))) MARK(cons1(z0, cons1(2nd(2nd(2nd(y0))), y1))) -> c11(MARK(cons1(2nd(2nd(2nd(y0))), y1))) MARK(cons1(z0, cons1(2nd(2nd(from(y0))), y1))) -> c11(MARK(cons1(2nd(2nd(from(y0))), y1))) MARK(cons1(z0, cons1(2nd(2nd(cons(y0, y1))), y2))) -> c11(MARK(cons1(2nd(2nd(cons(y0, y1))), y2))) MARK(cons1(z0, cons1(2nd(2nd(s(y0))), y1))) -> c11(MARK(cons1(2nd(2nd(s(y0))), y1))) MARK(cons1(z0, cons1(2nd(2nd(cons1(y0, y1))), y2))) -> c11(MARK(cons1(2nd(2nd(cons1(y0, y1))), y2))) MARK(cons1(z0, cons1(2nd(2nd(y0)), y1))) -> c11(MARK(cons1(2nd(2nd(y0)), y1))) MARK(cons1(z0, cons1(2nd(from(y0)), y1))) -> c11(MARK(cons1(2nd(from(y0)), y1))) MARK(cons1(z0, cons1(2nd(from(2nd(y0))), y1))) -> c11(MARK(cons1(2nd(from(2nd(y0))), y1))) MARK(cons1(z0, cons1(2nd(from(from(y0))), y1))) -> c11(MARK(cons1(2nd(from(from(y0))), y1))) MARK(cons1(z0, cons1(2nd(from(cons(y0, y1))), y2))) -> c11(MARK(cons1(2nd(from(cons(y0, y1))), y2))) MARK(cons1(z0, cons1(2nd(from(s(y0))), y1))) -> c11(MARK(cons1(2nd(from(s(y0))), y1))) MARK(cons1(z0, cons1(2nd(from(cons1(y0, y1))), y2))) -> c11(MARK(cons1(2nd(from(cons1(y0, y1))), y2))) MARK(cons1(z0, cons1(2nd(cons1(y0, 2nd(y1))), y2))) -> c11(MARK(cons1(2nd(cons1(y0, 2nd(y1))), y2))) MARK(cons1(z0, cons1(2nd(cons1(y0, from(y1))), y2))) -> c11(MARK(cons1(2nd(cons1(y0, from(y1))), y2))) MARK(cons1(z0, cons1(2nd(cons1(y0, cons(y1, y2))), y3))) -> c11(MARK(cons1(2nd(cons1(y0, cons(y1, y2))), y3))) MARK(cons1(z0, cons1(2nd(cons1(2nd(y0), y1)), y2))) -> c11(MARK(cons1(2nd(cons1(2nd(y0), y1)), y2))) MARK(cons1(z0, cons1(2nd(cons1(from(y0), y1)), y2))) -> c11(MARK(cons1(2nd(cons1(from(y0), y1)), y2))) MARK(cons1(z0, cons1(2nd(cons1(cons(y0, y1), y2)), y3))) -> c11(MARK(cons1(2nd(cons1(cons(y0, y1), y2)), y3))) MARK(cons1(z0, cons1(2nd(cons1(s(y0), y1)), y2))) -> c11(MARK(cons1(2nd(cons1(s(y0), y1)), y2))) MARK(cons1(z0, cons1(2nd(cons1(cons1(y0, y1), y2)), y3))) -> c11(MARK(cons1(2nd(cons1(cons1(y0, y1), y2)), y3))) MARK(cons1(z0, cons1(2nd(cons1(y0, y1)), y2))) -> c11(MARK(cons1(2nd(cons1(y0, y1)), y2))) MARK(cons1(z0, cons1(2nd(cons1(y0, s(y1))), y2))) -> c11(MARK(cons1(2nd(cons1(y0, s(y1))), y2))) MARK(cons1(z0, cons1(2nd(cons1(y0, cons1(y1, y2))), y3))) -> c11(MARK(cons1(2nd(cons1(y0, cons1(y1, y2))), y3))) MARK(cons1(z0, cons1(from(cons(y0, y1)), y2))) -> c11(MARK(cons1(from(cons(y0, y1)), y2))) MARK(cons1(z0, cons1(from(s(y0)), y1))) -> c11(MARK(cons1(from(s(y0)), y1))) MARK(cons1(z0, cons1(from(cons1(y0, y1)), y2))) -> c11(MARK(cons1(from(cons1(y0, y1)), y2))) MARK(cons1(z0, cons1(from(2nd(y0)), y1))) -> c11(MARK(cons1(from(2nd(y0)), y1))) MARK(cons1(z0, cons1(from(2nd(2nd(y0))), y1))) -> c11(MARK(cons1(from(2nd(2nd(y0))), y1))) MARK(cons1(z0, cons1(from(2nd(from(y0))), y1))) -> c11(MARK(cons1(from(2nd(from(y0))), y1))) MARK(cons1(z0, cons1(from(2nd(cons(y0, y1))), y2))) -> c11(MARK(cons1(from(2nd(cons(y0, y1))), y2))) MARK(cons1(z0, cons1(from(2nd(s(y0))), y1))) -> c11(MARK(cons1(from(2nd(s(y0))), y1))) MARK(cons1(z0, cons1(from(2nd(cons1(y0, y1))), y2))) -> c11(MARK(cons1(from(2nd(cons1(y0, y1))), y2))) MARK(cons1(z0, cons1(from(from(y0)), y1))) -> c11(MARK(cons1(from(from(y0)), y1))) MARK(cons1(z0, cons1(from(from(2nd(y0))), y1))) -> c11(MARK(cons1(from(from(2nd(y0))), y1))) MARK(cons1(z0, cons1(from(from(from(y0))), y1))) -> c11(MARK(cons1(from(from(from(y0))), y1))) MARK(cons1(z0, cons1(from(from(cons(y0, y1))), y2))) -> c11(MARK(cons1(from(from(cons(y0, y1))), y2))) MARK(cons1(z0, cons1(from(from(s(y0))), y1))) -> c11(MARK(cons1(from(from(s(y0))), y1))) MARK(cons1(z0, cons1(from(from(cons1(y0, y1))), y2))) -> c11(MARK(cons1(from(from(cons1(y0, y1))), y2))) MARK(cons1(z0, cons1(cons(cons(y0, y1), y2), y3))) -> c11(MARK(cons1(cons(cons(y0, y1), y2), y3))) MARK(cons1(z0, cons1(cons(s(y0), y1), y2))) -> c11(MARK(cons1(cons(s(y0), y1), y2))) MARK(cons1(z0, cons1(cons(cons1(y0, y1), y2), y3))) -> c11(MARK(cons1(cons(cons1(y0, y1), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(cons(y0, y1)), y2), y3))) -> c11(MARK(cons1(cons(2nd(cons(y0, y1)), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(s(y0)), y1), y2))) -> c11(MARK(cons1(cons(2nd(s(y0)), y1), y2))) MARK(cons1(z0, cons1(cons(2nd(2nd(2nd(y0))), y1), y2))) -> c11(MARK(cons1(cons(2nd(2nd(2nd(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(2nd(2nd(from(y0))), y1), y2))) -> c11(MARK(cons1(cons(2nd(2nd(from(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(2nd(2nd(cons(y0, y1))), y2), y3))) -> c11(MARK(cons1(cons(2nd(2nd(cons(y0, y1))), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(2nd(s(y0))), y1), y2))) -> c11(MARK(cons1(cons(2nd(2nd(s(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(2nd(2nd(cons1(y0, y1))), y2), y3))) -> c11(MARK(cons1(cons(2nd(2nd(cons1(y0, y1))), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(2nd(y0)), y1), y2))) -> c11(MARK(cons1(cons(2nd(2nd(y0)), y1), y2))) MARK(cons1(z0, cons1(cons(2nd(from(y0)), y1), y2))) -> c11(MARK(cons1(cons(2nd(from(y0)), y1), y2))) MARK(cons1(z0, cons1(cons(2nd(from(2nd(y0))), y1), y2))) -> c11(MARK(cons1(cons(2nd(from(2nd(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(2nd(from(from(y0))), y1), y2))) -> c11(MARK(cons1(cons(2nd(from(from(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(2nd(from(cons(y0, y1))), y2), y3))) -> c11(MARK(cons1(cons(2nd(from(cons(y0, y1))), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(from(s(y0))), y1), y2))) -> c11(MARK(cons1(cons(2nd(from(s(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(2nd(from(cons1(y0, y1))), y2), y3))) -> c11(MARK(cons1(cons(2nd(from(cons1(y0, y1))), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(cons1(y0, 2nd(y1))), y2), y3))) -> c11(MARK(cons1(cons(2nd(cons1(y0, 2nd(y1))), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(cons1(y0, from(y1))), y2), y3))) -> c11(MARK(cons1(cons(2nd(cons1(y0, from(y1))), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(cons1(y0, cons(y1, y2))), y3), y4))) -> c11(MARK(cons1(cons(2nd(cons1(y0, cons(y1, y2))), y3), y4))) MARK(cons1(z0, cons1(cons(2nd(cons1(2nd(y0), y1)), y2), y3))) -> c11(MARK(cons1(cons(2nd(cons1(2nd(y0), y1)), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(cons1(from(y0), y1)), y2), y3))) -> c11(MARK(cons1(cons(2nd(cons1(from(y0), y1)), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(cons1(cons(y0, y1), y2)), y3), y4))) -> c11(MARK(cons1(cons(2nd(cons1(cons(y0, y1), y2)), y3), y4))) MARK(cons1(z0, cons1(cons(2nd(cons1(s(y0), y1)), y2), y3))) -> c11(MARK(cons1(cons(2nd(cons1(s(y0), y1)), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(cons1(cons1(y0, y1), y2)), y3), y4))) -> c11(MARK(cons1(cons(2nd(cons1(cons1(y0, y1), y2)), y3), y4))) MARK(cons1(z0, cons1(cons(2nd(cons1(y0, y1)), y2), y3))) -> c11(MARK(cons1(cons(2nd(cons1(y0, y1)), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(cons1(y0, s(y1))), y2), y3))) -> c11(MARK(cons1(cons(2nd(cons1(y0, s(y1))), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(cons1(y0, cons1(y1, y2))), y3), y4))) -> c11(MARK(cons1(cons(2nd(cons1(y0, cons1(y1, y2))), y3), y4))) MARK(cons1(z0, cons1(cons(from(cons(y0, y1)), y2), y3))) -> c11(MARK(cons1(cons(from(cons(y0, y1)), y2), y3))) MARK(cons1(z0, cons1(cons(from(s(y0)), y1), y2))) -> c11(MARK(cons1(cons(from(s(y0)), y1), y2))) MARK(cons1(z0, cons1(cons(from(cons1(y0, y1)), y2), y3))) -> c11(MARK(cons1(cons(from(cons1(y0, y1)), y2), y3))) MARK(cons1(z0, cons1(cons(from(2nd(y0)), y1), y2))) -> c11(MARK(cons1(cons(from(2nd(y0)), y1), y2))) MARK(cons1(z0, cons1(cons(from(2nd(2nd(y0))), y1), y2))) -> c11(MARK(cons1(cons(from(2nd(2nd(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(from(2nd(from(y0))), y1), y2))) -> c11(MARK(cons1(cons(from(2nd(from(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(from(2nd(cons(y0, y1))), y2), y3))) -> c11(MARK(cons1(cons(from(2nd(cons(y0, y1))), y2), y3))) MARK(cons1(z0, cons1(cons(from(2nd(s(y0))), y1), y2))) -> c11(MARK(cons1(cons(from(2nd(s(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(from(2nd(cons1(y0, y1))), y2), y3))) -> c11(MARK(cons1(cons(from(2nd(cons1(y0, y1))), y2), y3))) MARK(cons1(z0, cons1(cons(from(from(y0)), y1), y2))) -> c11(MARK(cons1(cons(from(from(y0)), y1), y2))) MARK(cons1(z0, cons1(cons(from(from(2nd(y0))), y1), y2))) -> c11(MARK(cons1(cons(from(from(2nd(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(from(from(from(y0))), y1), y2))) -> c11(MARK(cons1(cons(from(from(from(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(from(from(cons(y0, y1))), y2), y3))) -> c11(MARK(cons1(cons(from(from(cons(y0, y1))), y2), y3))) MARK(cons1(z0, cons1(cons(from(from(s(y0))), y1), y2))) -> c11(MARK(cons1(cons(from(from(s(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(from(from(cons1(y0, y1))), y2), y3))) -> c11(MARK(cons1(cons(from(from(cons1(y0, y1))), y2), y3))) MARK(cons1(z0, cons1(s(s(y0)), y1))) -> c11(MARK(cons1(s(s(y0)), y1))) MARK(cons1(z0, cons1(s(cons1(y0, y1)), y2))) -> c11(MARK(cons1(s(cons1(y0, y1)), y2))) MARK(cons1(z0, cons1(s(2nd(cons(y0, y1))), y2))) -> c11(MARK(cons1(s(2nd(cons(y0, y1))), y2))) MARK(cons1(z0, cons1(s(2nd(s(y0))), y1))) -> c11(MARK(cons1(s(2nd(s(y0))), y1))) MARK(cons1(z0, cons1(s(2nd(2nd(2nd(y0)))), y1))) -> c11(MARK(cons1(s(2nd(2nd(2nd(y0)))), y1))) MARK(cons1(z0, cons1(s(2nd(2nd(from(y0)))), y1))) -> c11(MARK(cons1(s(2nd(2nd(from(y0)))), y1))) MARK(cons1(z0, cons1(s(2nd(2nd(cons(y0, y1)))), y2))) -> c11(MARK(cons1(s(2nd(2nd(cons(y0, y1)))), y2))) MARK(cons1(z0, cons1(s(2nd(2nd(s(y0)))), y1))) -> c11(MARK(cons1(s(2nd(2nd(s(y0)))), y1))) MARK(cons1(z0, cons1(s(2nd(2nd(cons1(y0, y1)))), y2))) -> c11(MARK(cons1(s(2nd(2nd(cons1(y0, y1)))), y2))) MARK(cons1(z0, cons1(s(2nd(2nd(y0))), y1))) -> c11(MARK(cons1(s(2nd(2nd(y0))), y1))) MARK(cons1(z0, cons1(s(2nd(from(y0))), y1))) -> c11(MARK(cons1(s(2nd(from(y0))), y1))) MARK(cons1(z0, cons1(s(2nd(from(2nd(y0)))), y1))) -> c11(MARK(cons1(s(2nd(from(2nd(y0)))), y1))) MARK(cons1(z0, cons1(s(2nd(from(from(y0)))), y1))) -> c11(MARK(cons1(s(2nd(from(from(y0)))), y1))) MARK(cons1(z0, cons1(s(2nd(from(cons(y0, y1)))), y2))) -> c11(MARK(cons1(s(2nd(from(cons(y0, y1)))), y2))) MARK(cons1(z0, cons1(s(2nd(from(s(y0)))), y1))) -> c11(MARK(cons1(s(2nd(from(s(y0)))), y1))) MARK(cons1(z0, cons1(s(2nd(from(cons1(y0, y1)))), y2))) -> c11(MARK(cons1(s(2nd(from(cons1(y0, y1)))), y2))) MARK(cons1(z0, cons1(s(2nd(cons1(y0, 2nd(y1)))), y2))) -> c11(MARK(cons1(s(2nd(cons1(y0, 2nd(y1)))), y2))) MARK(cons1(z0, cons1(s(2nd(cons1(y0, from(y1)))), y2))) -> c11(MARK(cons1(s(2nd(cons1(y0, from(y1)))), y2))) MARK(cons1(z0, cons1(s(2nd(cons1(y0, cons(y1, y2)))), y3))) -> c11(MARK(cons1(s(2nd(cons1(y0, cons(y1, y2)))), y3))) MARK(cons1(z0, cons1(s(2nd(cons1(2nd(y0), y1))), y2))) -> c11(MARK(cons1(s(2nd(cons1(2nd(y0), y1))), y2))) MARK(cons1(z0, cons1(s(2nd(cons1(from(y0), y1))), y2))) -> c11(MARK(cons1(s(2nd(cons1(from(y0), y1))), y2))) MARK(cons1(z0, cons1(s(2nd(cons1(cons(y0, y1), y2))), y3))) -> c11(MARK(cons1(s(2nd(cons1(cons(y0, y1), y2))), y3))) MARK(cons1(z0, cons1(s(2nd(cons1(s(y0), y1))), y2))) -> c11(MARK(cons1(s(2nd(cons1(s(y0), y1))), y2))) MARK(cons1(z0, cons1(s(2nd(cons1(cons1(y0, y1), y2))), y3))) -> c11(MARK(cons1(s(2nd(cons1(cons1(y0, y1), y2))), y3))) MARK(cons1(z0, cons1(s(2nd(cons1(y0, y1))), y2))) -> c11(MARK(cons1(s(2nd(cons1(y0, y1))), y2))) MARK(cons1(z0, cons1(s(2nd(cons1(y0, s(y1)))), y2))) -> c11(MARK(cons1(s(2nd(cons1(y0, s(y1)))), y2))) MARK(cons1(z0, cons1(s(2nd(cons1(y0, cons1(y1, y2)))), y3))) -> c11(MARK(cons1(s(2nd(cons1(y0, cons1(y1, y2)))), y3))) MARK(cons1(z0, cons1(s(from(cons(y0, y1))), y2))) -> c11(MARK(cons1(s(from(cons(y0, y1))), y2))) MARK(cons1(z0, cons1(s(from(s(y0))), y1))) -> c11(MARK(cons1(s(from(s(y0))), y1))) MARK(cons1(z0, cons1(s(from(cons1(y0, y1))), y2))) -> c11(MARK(cons1(s(from(cons1(y0, y1))), y2))) MARK(cons1(z0, cons1(s(from(2nd(y0))), y1))) -> c11(MARK(cons1(s(from(2nd(y0))), y1))) MARK(cons1(z0, cons1(s(from(2nd(2nd(y0)))), y1))) -> c11(MARK(cons1(s(from(2nd(2nd(y0)))), y1))) MARK(cons1(z0, cons1(s(from(2nd(from(y0)))), y1))) -> c11(MARK(cons1(s(from(2nd(from(y0)))), y1))) MARK(cons1(z0, cons1(s(from(2nd(cons(y0, y1)))), y2))) -> c11(MARK(cons1(s(from(2nd(cons(y0, y1)))), y2))) MARK(cons1(z0, cons1(s(from(2nd(s(y0)))), y1))) -> c11(MARK(cons1(s(from(2nd(s(y0)))), y1))) MARK(cons1(z0, cons1(s(from(2nd(cons1(y0, y1)))), y2))) -> c11(MARK(cons1(s(from(2nd(cons1(y0, y1)))), y2))) MARK(cons1(z0, cons1(s(from(from(y0))), y1))) -> c11(MARK(cons1(s(from(from(y0))), y1))) MARK(cons1(z0, cons1(s(from(from(2nd(y0)))), y1))) -> c11(MARK(cons1(s(from(from(2nd(y0)))), y1))) MARK(cons1(z0, cons1(s(from(from(from(y0)))), y1))) -> c11(MARK(cons1(s(from(from(from(y0)))), y1))) MARK(cons1(z0, cons1(s(from(from(cons(y0, y1)))), y2))) -> c11(MARK(cons1(s(from(from(cons(y0, y1)))), y2))) MARK(cons1(z0, cons1(s(from(from(s(y0)))), y1))) -> c11(MARK(cons1(s(from(from(s(y0)))), y1))) MARK(cons1(z0, cons1(s(from(from(cons1(y0, y1)))), y2))) -> c11(MARK(cons1(s(from(from(cons1(y0, y1)))), y2))) MARK(cons1(z0, cons1(s(cons(cons(y0, y1), y2)), y3))) -> c11(MARK(cons1(s(cons(cons(y0, y1), y2)), y3))) MARK(cons1(z0, cons1(s(cons(s(y0), y1)), y2))) -> c11(MARK(cons1(s(cons(s(y0), y1)), y2))) MARK(cons1(z0, cons1(s(cons(cons1(y0, y1), y2)), y3))) -> c11(MARK(cons1(s(cons(cons1(y0, y1), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(cons(y0, y1)), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(cons(y0, y1)), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(s(y0)), y1)), y2))) -> c11(MARK(cons1(s(cons(2nd(s(y0)), y1)), y2))) MARK(cons1(z0, cons1(s(cons(2nd(2nd(2nd(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(2nd(2nd(2nd(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(2nd(2nd(from(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(2nd(2nd(from(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(2nd(2nd(cons(y0, y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(2nd(cons(y0, y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(2nd(s(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(2nd(2nd(s(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(2nd(2nd(cons1(y0, y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(2nd(cons1(y0, y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(2nd(y0)), y1)), y2))) -> c11(MARK(cons1(s(cons(2nd(2nd(y0)), y1)), y2))) MARK(cons1(z0, cons1(s(cons(2nd(from(y0)), y1)), y2))) -> c11(MARK(cons1(s(cons(2nd(from(y0)), y1)), y2))) MARK(cons1(z0, cons1(s(cons(2nd(from(2nd(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(2nd(from(2nd(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(2nd(from(from(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(2nd(from(from(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(2nd(from(cons(y0, y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(from(cons(y0, y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(from(s(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(2nd(from(s(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(2nd(from(cons1(y0, y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(from(cons1(y0, y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(y0, 2nd(y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(cons1(y0, 2nd(y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(y0, from(y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(cons1(y0, from(y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(y0, cons(y1, y2))), y3)), y4))) -> c11(MARK(cons1(s(cons(2nd(cons1(y0, cons(y1, y2))), y3)), y4))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(2nd(y0), y1)), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(cons1(2nd(y0), y1)), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(from(y0), y1)), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(cons1(from(y0), y1)), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(cons(y0, y1), y2)), y3)), y4))) -> c11(MARK(cons1(s(cons(2nd(cons1(cons(y0, y1), y2)), y3)), y4))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(s(y0), y1)), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(cons1(s(y0), y1)), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(cons1(y0, y1), y2)), y3)), y4))) -> c11(MARK(cons1(s(cons(2nd(cons1(cons1(y0, y1), y2)), y3)), y4))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(y0, y1)), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(cons1(y0, y1)), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(y0, s(y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(cons1(y0, s(y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(y0, cons1(y1, y2))), y3)), y4))) -> c11(MARK(cons1(s(cons(2nd(cons1(y0, cons1(y1, y2))), y3)), y4))) MARK(cons1(z0, cons1(s(cons(from(cons(y0, y1)), y2)), y3))) -> c11(MARK(cons1(s(cons(from(cons(y0, y1)), y2)), y3))) MARK(cons1(z0, cons1(s(cons(from(s(y0)), y1)), y2))) -> c11(MARK(cons1(s(cons(from(s(y0)), y1)), y2))) MARK(cons1(z0, cons1(s(cons(from(cons1(y0, y1)), y2)), y3))) -> c11(MARK(cons1(s(cons(from(cons1(y0, y1)), y2)), y3))) MARK(cons1(z0, cons1(s(cons(from(2nd(y0)), y1)), y2))) -> c11(MARK(cons1(s(cons(from(2nd(y0)), y1)), y2))) MARK(cons1(z0, cons1(s(cons(from(2nd(2nd(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(from(2nd(2nd(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(from(2nd(from(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(from(2nd(from(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(from(2nd(cons(y0, y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(from(2nd(cons(y0, y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(from(2nd(s(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(from(2nd(s(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(from(2nd(cons1(y0, y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(from(2nd(cons1(y0, y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(from(from(y0)), y1)), y2))) -> c11(MARK(cons1(s(cons(from(from(y0)), y1)), y2))) MARK(cons1(z0, cons1(s(cons(from(from(2nd(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(from(from(2nd(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(from(from(from(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(from(from(from(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(from(from(cons(y0, y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(from(from(cons(y0, y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(from(from(s(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(from(from(s(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(from(from(cons1(y0, y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(from(from(cons1(y0, y1))), y2)), y3))) ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: a__2nd(cons1(z0, cons(z1, z2))) -> mark(z1) a__2nd(cons(z0, z1)) -> a__2nd(cons1(mark(z0), mark(z1))) a__2nd(z0) -> 2nd(z0) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(2nd(z0)) -> a__2nd(mark(z0)) mark(from(z0)) -> a__from(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(cons1(z0, z1)) -> cons1(mark(z0), mark(z1)) Tuples: A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) MARK(2nd(cons1(x0, 2nd(z0)))) -> c6(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(cons1(x0, 2nd(z0)))) MARK(2nd(cons1(x0, from(z0)))) -> c6(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(cons1(x0, from(z0)))) MARK(2nd(cons1(x0, cons(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons1(x0, cons(z0, z1)))) MARK(2nd(cons1(2nd(z0), x1))) -> c6(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(cons1(2nd(z0), x1))) MARK(2nd(cons1(from(z0), x1))) -> c6(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(cons1(from(z0), x1))) MARK(2nd(cons1(cons(z0, z1), x1))) -> c6(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons1(cons(z0, z1), x1))) MARK(2nd(cons1(s(z0), x1))) -> c6(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(cons1(s(z0), x1))) MARK(2nd(cons1(cons1(z0, z1), x1))) -> c6(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(cons1(z0, z1), x1))) MARK(2nd(cons1(x0, x1))) -> c6(MARK(cons1(x0, x1))) MARK(2nd(cons1(x0, s(z0)))) -> c6(MARK(cons1(x0, s(z0)))) MARK(2nd(cons1(x0, cons1(z0, z1)))) -> c6(MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons1(z0, cons(from(y0), z2))) -> c(MARK(from(y0))) A__2ND(cons1(z0, cons(cons(y0, y1), z2))) -> c(MARK(cons(y0, y1))) A__2ND(cons1(z0, cons(s(y0), z2))) -> c(MARK(s(y0))) A__2ND(cons1(z0, cons(cons1(y0, y1), z2))) -> c(MARK(cons1(y0, y1))) A__2ND(cons1(z0, cons(2nd(cons(y0, y1)), z2))) -> c(MARK(2nd(cons(y0, y1)))) A__2ND(cons1(z0, cons(2nd(s(y0)), z2))) -> c(MARK(2nd(s(y0)))) A__2ND(cons1(z0, cons(2nd(2nd(2nd(y0))), z2))) -> c(MARK(2nd(2nd(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(from(y0))), z2))) -> c(MARK(2nd(2nd(from(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(s(y0))), z2))) -> c(MARK(2nd(2nd(s(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons1(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(y0)), z2))) -> c(MARK(2nd(2nd(y0)))) A__2ND(cons1(z0, cons(2nd(from(y0)), z2))) -> c(MARK(2nd(from(y0)))) A__2ND(cons1(z0, cons(2nd(from(2nd(y0))), z2))) -> c(MARK(2nd(from(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(from(from(y0))), z2))) -> c(MARK(2nd(from(from(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons(y0, y1))), z2))) -> c(MARK(2nd(from(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(from(s(y0))), z2))) -> c(MARK(2nd(from(s(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons1(y0, y1))), z2))) -> c(MARK(2nd(from(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, 2nd(y1))), z2))) -> c(MARK(2nd(cons1(y0, 2nd(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, from(y1))), z2))) -> c(MARK(2nd(cons1(y0, from(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons(y1, y2))))) A__2ND(cons1(z0, cons(2nd(cons1(2nd(y0), y1)), z2))) -> c(MARK(2nd(cons1(2nd(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(from(y0), y1)), z2))) -> c(MARK(2nd(cons1(from(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(s(y0), y1)), z2))) -> c(MARK(2nd(cons1(s(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons1(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, y1)), z2))) -> c(MARK(2nd(cons1(y0, y1)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, s(y1))), z2))) -> c(MARK(2nd(cons1(y0, s(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons1(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons1(y1, y2))))) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(from(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(x0)) A__2ND(cons(x0, cons(s(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(x0)) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(cons(2nd(z0), x2))) A__2ND(cons(x0, cons(from(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(cons(from(z0), x2))) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(cons(cons(z0, z1), x2))) A__2ND(cons(x0, cons(s(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(cons(s(z0), x2))) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(cons(cons1(z0, z1), x2))) A__2ND(cons(x0, cons(x1, x2))) -> c2(MARK(cons(x1, x2))) A__FROM(from(y0)) -> c4(MARK(from(y0))) A__FROM(cons(y0, y1)) -> c4(MARK(cons(y0, y1))) A__FROM(s(y0)) -> c4(MARK(s(y0))) A__FROM(cons1(y0, y1)) -> c4(MARK(cons1(y0, y1))) A__FROM(2nd(cons(y0, y1))) -> c4(MARK(2nd(cons(y0, y1)))) A__FROM(2nd(s(y0))) -> c4(MARK(2nd(s(y0)))) A__FROM(2nd(2nd(2nd(y0)))) -> c4(MARK(2nd(2nd(2nd(y0))))) A__FROM(2nd(2nd(from(y0)))) -> c4(MARK(2nd(2nd(from(y0))))) A__FROM(2nd(2nd(cons(y0, y1)))) -> c4(MARK(2nd(2nd(cons(y0, y1))))) A__FROM(2nd(2nd(s(y0)))) -> c4(MARK(2nd(2nd(s(y0))))) A__FROM(2nd(2nd(cons1(y0, y1)))) -> c4(MARK(2nd(2nd(cons1(y0, y1))))) A__FROM(2nd(2nd(y0))) -> c4(MARK(2nd(2nd(y0)))) A__FROM(2nd(from(y0))) -> c4(MARK(2nd(from(y0)))) A__FROM(2nd(from(2nd(y0)))) -> c4(MARK(2nd(from(2nd(y0))))) A__FROM(2nd(from(from(y0)))) -> c4(MARK(2nd(from(from(y0))))) A__FROM(2nd(from(cons(y0, y1)))) -> c4(MARK(2nd(from(cons(y0, y1))))) A__FROM(2nd(from(s(y0)))) -> c4(MARK(2nd(from(s(y0))))) A__FROM(2nd(from(cons1(y0, y1)))) -> c4(MARK(2nd(from(cons1(y0, y1))))) A__FROM(2nd(cons1(y0, 2nd(y1)))) -> c4(MARK(2nd(cons1(y0, 2nd(y1))))) A__FROM(2nd(cons1(y0, from(y1)))) -> c4(MARK(2nd(cons1(y0, from(y1))))) A__FROM(2nd(cons1(y0, cons(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons(y1, y2))))) A__FROM(2nd(cons1(2nd(y0), y1))) -> c4(MARK(2nd(cons1(2nd(y0), y1)))) A__FROM(2nd(cons1(from(y0), y1))) -> c4(MARK(2nd(cons1(from(y0), y1)))) A__FROM(2nd(cons1(cons(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons(y0, y1), y2)))) A__FROM(2nd(cons1(s(y0), y1))) -> c4(MARK(2nd(cons1(s(y0), y1)))) A__FROM(2nd(cons1(cons1(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__FROM(2nd(cons1(y0, y1))) -> c4(MARK(2nd(cons1(y0, y1)))) A__FROM(2nd(cons1(y0, s(y1)))) -> c4(MARK(2nd(cons1(y0, s(y1))))) A__FROM(2nd(cons1(y0, cons1(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons1(z0, z1))) -> c7(A__FROM(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(from(2nd(x0))) -> c7(A__FROM(2nd(mark(x0))), MARK(2nd(x0))) MARK(from(2nd(2nd(z0)))) -> c7(A__FROM(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(from(2nd(from(z0)))) -> c7(A__FROM(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(from(2nd(cons(z0, z1)))) -> c7(A__FROM(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(from(2nd(s(z0)))) -> c7(A__FROM(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(from(2nd(cons1(z0, z1)))) -> c7(A__FROM(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(from(from(x0))) -> c7(A__FROM(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(from(from(x0))) -> c7(A__FROM(from(mark(x0))), MARK(from(x0))) MARK(from(from(2nd(z0)))) -> c7(A__FROM(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(from(from(from(z0)))) -> c7(A__FROM(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(from(from(cons(z0, z1)))) -> c7(A__FROM(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(from(from(s(z0)))) -> c7(A__FROM(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(from(from(cons1(z0, z1)))) -> c7(A__FROM(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(cons(cons(y0, y1), z1)) -> c8(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c8(MARK(s(y0))) MARK(cons(cons1(y0, y1), z1)) -> c8(MARK(cons1(y0, y1))) MARK(cons(2nd(cons(y0, y1)), z1)) -> c8(MARK(2nd(cons(y0, y1)))) MARK(cons(2nd(s(y0)), z1)) -> c8(MARK(2nd(s(y0)))) MARK(cons(2nd(2nd(2nd(y0))), z1)) -> c8(MARK(2nd(2nd(2nd(y0))))) MARK(cons(2nd(2nd(from(y0))), z1)) -> c8(MARK(2nd(2nd(from(y0))))) MARK(cons(2nd(2nd(cons(y0, y1))), z1)) -> c8(MARK(2nd(2nd(cons(y0, y1))))) MARK(cons(2nd(2nd(s(y0))), z1)) -> c8(MARK(2nd(2nd(s(y0))))) MARK(cons(2nd(2nd(cons1(y0, y1))), z1)) -> c8(MARK(2nd(2nd(cons1(y0, y1))))) MARK(cons(2nd(2nd(y0)), z1)) -> c8(MARK(2nd(2nd(y0)))) MARK(cons(2nd(from(y0)), z1)) -> c8(MARK(2nd(from(y0)))) MARK(cons(2nd(from(2nd(y0))), z1)) -> c8(MARK(2nd(from(2nd(y0))))) MARK(cons(2nd(from(from(y0))), z1)) -> c8(MARK(2nd(from(from(y0))))) MARK(cons(2nd(from(cons(y0, y1))), z1)) -> c8(MARK(2nd(from(cons(y0, y1))))) MARK(cons(2nd(from(s(y0))), z1)) -> c8(MARK(2nd(from(s(y0))))) MARK(cons(2nd(from(cons1(y0, y1))), z1)) -> c8(MARK(2nd(from(cons1(y0, y1))))) MARK(cons(2nd(cons1(y0, 2nd(y1))), z1)) -> c8(MARK(2nd(cons1(y0, 2nd(y1))))) MARK(cons(2nd(cons1(y0, from(y1))), z1)) -> c8(MARK(2nd(cons1(y0, from(y1))))) MARK(cons(2nd(cons1(y0, cons(y1, y2))), z1)) -> c8(MARK(2nd(cons1(y0, cons(y1, y2))))) MARK(cons(2nd(cons1(2nd(y0), y1)), z1)) -> c8(MARK(2nd(cons1(2nd(y0), y1)))) MARK(cons(2nd(cons1(from(y0), y1)), z1)) -> c8(MARK(2nd(cons1(from(y0), y1)))) MARK(cons(2nd(cons1(cons(y0, y1), y2)), z1)) -> c8(MARK(2nd(cons1(cons(y0, y1), y2)))) MARK(cons(2nd(cons1(s(y0), y1)), z1)) -> c8(MARK(2nd(cons1(s(y0), y1)))) MARK(cons(2nd(cons1(cons1(y0, y1), y2)), z1)) -> c8(MARK(2nd(cons1(cons1(y0, y1), y2)))) MARK(cons(2nd(cons1(y0, y1)), z1)) -> c8(MARK(2nd(cons1(y0, y1)))) MARK(cons(2nd(cons1(y0, s(y1))), z1)) -> c8(MARK(2nd(cons1(y0, s(y1))))) MARK(cons(2nd(cons1(y0, cons1(y1, y2))), z1)) -> c8(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(cons(from(cons(y0, y1)), z1)) -> c8(MARK(from(cons(y0, y1)))) MARK(cons(from(s(y0)), z1)) -> c8(MARK(from(s(y0)))) MARK(cons(from(cons1(y0, y1)), z1)) -> c8(MARK(from(cons1(y0, y1)))) MARK(cons(from(2nd(y0)), z1)) -> c8(MARK(from(2nd(y0)))) MARK(cons(from(2nd(2nd(y0))), z1)) -> c8(MARK(from(2nd(2nd(y0))))) MARK(cons(from(2nd(from(y0))), z1)) -> c8(MARK(from(2nd(from(y0))))) MARK(cons(from(2nd(cons(y0, y1))), z1)) -> c8(MARK(from(2nd(cons(y0, y1))))) MARK(cons(from(2nd(s(y0))), z1)) -> c8(MARK(from(2nd(s(y0))))) MARK(cons(from(2nd(cons1(y0, y1))), z1)) -> c8(MARK(from(2nd(cons1(y0, y1))))) MARK(cons(from(from(y0)), z1)) -> c8(MARK(from(from(y0)))) MARK(cons(from(from(2nd(y0))), z1)) -> c8(MARK(from(from(2nd(y0))))) MARK(cons(from(from(from(y0))), z1)) -> c8(MARK(from(from(from(y0))))) MARK(cons(from(from(cons(y0, y1))), z1)) -> c8(MARK(from(from(cons(y0, y1))))) MARK(cons(from(from(s(y0))), z1)) -> c8(MARK(from(from(s(y0))))) MARK(cons(from(from(cons1(y0, y1))), z1)) -> c8(MARK(from(from(cons1(y0, y1))))) MARK(s(s(y0))) -> c9(MARK(s(y0))) MARK(s(cons1(y0, y1))) -> c9(MARK(cons1(y0, y1))) MARK(s(2nd(cons(y0, y1)))) -> c9(MARK(2nd(cons(y0, y1)))) MARK(s(2nd(s(y0)))) -> c9(MARK(2nd(s(y0)))) MARK(s(2nd(2nd(2nd(y0))))) -> c9(MARK(2nd(2nd(2nd(y0))))) MARK(s(2nd(2nd(from(y0))))) -> c9(MARK(2nd(2nd(from(y0))))) MARK(s(2nd(2nd(cons(y0, y1))))) -> c9(MARK(2nd(2nd(cons(y0, y1))))) MARK(s(2nd(2nd(s(y0))))) -> c9(MARK(2nd(2nd(s(y0))))) MARK(s(2nd(2nd(cons1(y0, y1))))) -> c9(MARK(2nd(2nd(cons1(y0, y1))))) MARK(s(2nd(2nd(y0)))) -> c9(MARK(2nd(2nd(y0)))) MARK(s(2nd(from(y0)))) -> c9(MARK(2nd(from(y0)))) MARK(s(2nd(from(2nd(y0))))) -> c9(MARK(2nd(from(2nd(y0))))) MARK(s(2nd(from(from(y0))))) -> c9(MARK(2nd(from(from(y0))))) MARK(s(2nd(from(cons(y0, y1))))) -> c9(MARK(2nd(from(cons(y0, y1))))) MARK(s(2nd(from(s(y0))))) -> c9(MARK(2nd(from(s(y0))))) MARK(s(2nd(from(cons1(y0, y1))))) -> c9(MARK(2nd(from(cons1(y0, y1))))) MARK(s(2nd(cons1(y0, 2nd(y1))))) -> c9(MARK(2nd(cons1(y0, 2nd(y1))))) MARK(s(2nd(cons1(y0, from(y1))))) -> c9(MARK(2nd(cons1(y0, from(y1))))) MARK(s(2nd(cons1(y0, cons(y1, y2))))) -> c9(MARK(2nd(cons1(y0, cons(y1, y2))))) MARK(s(2nd(cons1(2nd(y0), y1)))) -> c9(MARK(2nd(cons1(2nd(y0), y1)))) MARK(s(2nd(cons1(from(y0), y1)))) -> c9(MARK(2nd(cons1(from(y0), y1)))) MARK(s(2nd(cons1(cons(y0, y1), y2)))) -> c9(MARK(2nd(cons1(cons(y0, y1), y2)))) MARK(s(2nd(cons1(s(y0), y1)))) -> c9(MARK(2nd(cons1(s(y0), y1)))) MARK(s(2nd(cons1(cons1(y0, y1), y2)))) -> c9(MARK(2nd(cons1(cons1(y0, y1), y2)))) MARK(s(2nd(cons1(y0, y1)))) -> c9(MARK(2nd(cons1(y0, y1)))) MARK(s(2nd(cons1(y0, s(y1))))) -> c9(MARK(2nd(cons1(y0, s(y1))))) MARK(s(2nd(cons1(y0, cons1(y1, y2))))) -> c9(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(s(from(cons(y0, y1)))) -> c9(MARK(from(cons(y0, y1)))) MARK(s(from(s(y0)))) -> c9(MARK(from(s(y0)))) MARK(s(from(cons1(y0, y1)))) -> c9(MARK(from(cons1(y0, y1)))) MARK(s(from(2nd(y0)))) -> c9(MARK(from(2nd(y0)))) MARK(s(from(2nd(2nd(y0))))) -> c9(MARK(from(2nd(2nd(y0))))) MARK(s(from(2nd(from(y0))))) -> c9(MARK(from(2nd(from(y0))))) MARK(s(from(2nd(cons(y0, y1))))) -> c9(MARK(from(2nd(cons(y0, y1))))) MARK(s(from(2nd(s(y0))))) -> c9(MARK(from(2nd(s(y0))))) MARK(s(from(2nd(cons1(y0, y1))))) -> c9(MARK(from(2nd(cons1(y0, y1))))) MARK(s(from(from(y0)))) -> c9(MARK(from(from(y0)))) MARK(s(from(from(2nd(y0))))) -> c9(MARK(from(from(2nd(y0))))) MARK(s(from(from(from(y0))))) -> c9(MARK(from(from(from(y0))))) MARK(s(from(from(cons(y0, y1))))) -> c9(MARK(from(from(cons(y0, y1))))) MARK(s(from(from(s(y0))))) -> c9(MARK(from(from(s(y0))))) MARK(s(from(from(cons1(y0, y1))))) -> c9(MARK(from(from(cons1(y0, y1))))) MARK(s(cons(cons(y0, y1), y2))) -> c9(MARK(cons(cons(y0, y1), y2))) MARK(s(cons(s(y0), y1))) -> c9(MARK(cons(s(y0), y1))) MARK(s(cons(cons1(y0, y1), y2))) -> c9(MARK(cons(cons1(y0, y1), y2))) MARK(s(cons(2nd(cons(y0, y1)), y2))) -> c9(MARK(cons(2nd(cons(y0, y1)), y2))) MARK(s(cons(2nd(s(y0)), y1))) -> c9(MARK(cons(2nd(s(y0)), y1))) MARK(s(cons(2nd(2nd(2nd(y0))), y1))) -> c9(MARK(cons(2nd(2nd(2nd(y0))), y1))) MARK(s(cons(2nd(2nd(from(y0))), y1))) -> c9(MARK(cons(2nd(2nd(from(y0))), y1))) MARK(s(cons(2nd(2nd(cons(y0, y1))), y2))) -> c9(MARK(cons(2nd(2nd(cons(y0, y1))), y2))) MARK(s(cons(2nd(2nd(s(y0))), y1))) -> c9(MARK(cons(2nd(2nd(s(y0))), y1))) MARK(s(cons(2nd(2nd(cons1(y0, y1))), y2))) -> c9(MARK(cons(2nd(2nd(cons1(y0, y1))), y2))) MARK(s(cons(2nd(2nd(y0)), y1))) -> c9(MARK(cons(2nd(2nd(y0)), y1))) MARK(s(cons(2nd(from(y0)), y1))) -> c9(MARK(cons(2nd(from(y0)), y1))) MARK(s(cons(2nd(from(2nd(y0))), y1))) -> c9(MARK(cons(2nd(from(2nd(y0))), y1))) MARK(s(cons(2nd(from(from(y0))), y1))) -> c9(MARK(cons(2nd(from(from(y0))), y1))) MARK(s(cons(2nd(from(cons(y0, y1))), y2))) -> c9(MARK(cons(2nd(from(cons(y0, y1))), y2))) MARK(s(cons(2nd(from(s(y0))), y1))) -> c9(MARK(cons(2nd(from(s(y0))), y1))) MARK(s(cons(2nd(from(cons1(y0, y1))), y2))) -> c9(MARK(cons(2nd(from(cons1(y0, y1))), y2))) MARK(s(cons(2nd(cons1(y0, 2nd(y1))), y2))) -> c9(MARK(cons(2nd(cons1(y0, 2nd(y1))), y2))) MARK(s(cons(2nd(cons1(y0, from(y1))), y2))) -> c9(MARK(cons(2nd(cons1(y0, from(y1))), y2))) MARK(s(cons(2nd(cons1(y0, cons(y1, y2))), y3))) -> c9(MARK(cons(2nd(cons1(y0, cons(y1, y2))), y3))) MARK(s(cons(2nd(cons1(2nd(y0), y1)), y2))) -> c9(MARK(cons(2nd(cons1(2nd(y0), y1)), y2))) MARK(s(cons(2nd(cons1(from(y0), y1)), y2))) -> c9(MARK(cons(2nd(cons1(from(y0), y1)), y2))) MARK(s(cons(2nd(cons1(cons(y0, y1), y2)), y3))) -> c9(MARK(cons(2nd(cons1(cons(y0, y1), y2)), y3))) MARK(s(cons(2nd(cons1(s(y0), y1)), y2))) -> c9(MARK(cons(2nd(cons1(s(y0), y1)), y2))) MARK(s(cons(2nd(cons1(cons1(y0, y1), y2)), y3))) -> c9(MARK(cons(2nd(cons1(cons1(y0, y1), y2)), y3))) MARK(s(cons(2nd(cons1(y0, y1)), y2))) -> c9(MARK(cons(2nd(cons1(y0, y1)), y2))) MARK(s(cons(2nd(cons1(y0, s(y1))), y2))) -> c9(MARK(cons(2nd(cons1(y0, s(y1))), y2))) MARK(s(cons(2nd(cons1(y0, cons1(y1, y2))), y3))) -> c9(MARK(cons(2nd(cons1(y0, cons1(y1, y2))), y3))) MARK(s(cons(from(cons(y0, y1)), y2))) -> c9(MARK(cons(from(cons(y0, y1)), y2))) MARK(s(cons(from(s(y0)), y1))) -> c9(MARK(cons(from(s(y0)), y1))) MARK(s(cons(from(cons1(y0, y1)), y2))) -> c9(MARK(cons(from(cons1(y0, y1)), y2))) MARK(s(cons(from(2nd(y0)), y1))) -> c9(MARK(cons(from(2nd(y0)), y1))) MARK(s(cons(from(2nd(2nd(y0))), y1))) -> c9(MARK(cons(from(2nd(2nd(y0))), y1))) MARK(s(cons(from(2nd(from(y0))), y1))) -> c9(MARK(cons(from(2nd(from(y0))), y1))) MARK(s(cons(from(2nd(cons(y0, y1))), y2))) -> c9(MARK(cons(from(2nd(cons(y0, y1))), y2))) MARK(s(cons(from(2nd(s(y0))), y1))) -> c9(MARK(cons(from(2nd(s(y0))), y1))) MARK(s(cons(from(2nd(cons1(y0, y1))), y2))) -> c9(MARK(cons(from(2nd(cons1(y0, y1))), y2))) MARK(s(cons(from(from(y0)), y1))) -> c9(MARK(cons(from(from(y0)), y1))) MARK(s(cons(from(from(2nd(y0))), y1))) -> c9(MARK(cons(from(from(2nd(y0))), y1))) MARK(s(cons(from(from(from(y0))), y1))) -> c9(MARK(cons(from(from(from(y0))), y1))) MARK(s(cons(from(from(cons(y0, y1))), y2))) -> c9(MARK(cons(from(from(cons(y0, y1))), y2))) MARK(s(cons(from(from(s(y0))), y1))) -> c9(MARK(cons(from(from(s(y0))), y1))) MARK(s(cons(from(from(cons1(y0, y1))), y2))) -> c9(MARK(cons(from(from(cons1(y0, y1))), y2))) MARK(cons1(cons1(y0, y1), z1)) -> c10(MARK(cons1(y0, y1))) MARK(cons1(2nd(cons(y0, y1)), z1)) -> c10(MARK(2nd(cons(y0, y1)))) MARK(cons1(2nd(s(y0)), z1)) -> c10(MARK(2nd(s(y0)))) MARK(cons1(2nd(2nd(2nd(y0))), z1)) -> c10(MARK(2nd(2nd(2nd(y0))))) MARK(cons1(2nd(2nd(from(y0))), z1)) -> c10(MARK(2nd(2nd(from(y0))))) MARK(cons1(2nd(2nd(cons(y0, y1))), z1)) -> c10(MARK(2nd(2nd(cons(y0, y1))))) MARK(cons1(2nd(2nd(s(y0))), z1)) -> c10(MARK(2nd(2nd(s(y0))))) MARK(cons1(2nd(2nd(cons1(y0, y1))), z1)) -> c10(MARK(2nd(2nd(cons1(y0, y1))))) MARK(cons1(2nd(2nd(y0)), z1)) -> c10(MARK(2nd(2nd(y0)))) MARK(cons1(2nd(from(y0)), z1)) -> c10(MARK(2nd(from(y0)))) MARK(cons1(2nd(from(2nd(y0))), z1)) -> c10(MARK(2nd(from(2nd(y0))))) MARK(cons1(2nd(from(from(y0))), z1)) -> c10(MARK(2nd(from(from(y0))))) MARK(cons1(2nd(from(cons(y0, y1))), z1)) -> c10(MARK(2nd(from(cons(y0, y1))))) MARK(cons1(2nd(from(s(y0))), z1)) -> c10(MARK(2nd(from(s(y0))))) MARK(cons1(2nd(from(cons1(y0, y1))), z1)) -> c10(MARK(2nd(from(cons1(y0, y1))))) MARK(cons1(2nd(cons1(y0, 2nd(y1))), z1)) -> c10(MARK(2nd(cons1(y0, 2nd(y1))))) MARK(cons1(2nd(cons1(y0, from(y1))), z1)) -> c10(MARK(2nd(cons1(y0, from(y1))))) MARK(cons1(2nd(cons1(y0, cons(y1, y2))), z1)) -> c10(MARK(2nd(cons1(y0, cons(y1, y2))))) MARK(cons1(2nd(cons1(2nd(y0), y1)), z1)) -> c10(MARK(2nd(cons1(2nd(y0), y1)))) MARK(cons1(2nd(cons1(from(y0), y1)), z1)) -> c10(MARK(2nd(cons1(from(y0), y1)))) MARK(cons1(2nd(cons1(cons(y0, y1), y2)), z1)) -> c10(MARK(2nd(cons1(cons(y0, y1), y2)))) MARK(cons1(2nd(cons1(s(y0), y1)), z1)) -> c10(MARK(2nd(cons1(s(y0), y1)))) MARK(cons1(2nd(cons1(cons1(y0, y1), y2)), z1)) -> c10(MARK(2nd(cons1(cons1(y0, y1), y2)))) MARK(cons1(2nd(cons1(y0, y1)), z1)) -> c10(MARK(2nd(cons1(y0, y1)))) MARK(cons1(2nd(cons1(y0, s(y1))), z1)) -> c10(MARK(2nd(cons1(y0, s(y1))))) MARK(cons1(2nd(cons1(y0, cons1(y1, y2))), z1)) -> c10(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(cons1(from(cons(y0, y1)), z1)) -> c10(MARK(from(cons(y0, y1)))) MARK(cons1(from(s(y0)), z1)) -> c10(MARK(from(s(y0)))) MARK(cons1(from(cons1(y0, y1)), z1)) -> c10(MARK(from(cons1(y0, y1)))) MARK(cons1(from(2nd(y0)), z1)) -> c10(MARK(from(2nd(y0)))) MARK(cons1(from(2nd(2nd(y0))), z1)) -> c10(MARK(from(2nd(2nd(y0))))) MARK(cons1(from(2nd(from(y0))), z1)) -> c10(MARK(from(2nd(from(y0))))) MARK(cons1(from(2nd(cons(y0, y1))), z1)) -> c10(MARK(from(2nd(cons(y0, y1))))) MARK(cons1(from(2nd(s(y0))), z1)) -> c10(MARK(from(2nd(s(y0))))) MARK(cons1(from(2nd(cons1(y0, y1))), z1)) -> c10(MARK(from(2nd(cons1(y0, y1))))) MARK(cons1(from(from(y0)), z1)) -> c10(MARK(from(from(y0)))) MARK(cons1(from(from(2nd(y0))), z1)) -> c10(MARK(from(from(2nd(y0))))) MARK(cons1(from(from(from(y0))), z1)) -> c10(MARK(from(from(from(y0))))) MARK(cons1(from(from(cons(y0, y1))), z1)) -> c10(MARK(from(from(cons(y0, y1))))) MARK(cons1(from(from(s(y0))), z1)) -> c10(MARK(from(from(s(y0))))) MARK(cons1(from(from(cons1(y0, y1))), z1)) -> c10(MARK(from(from(cons1(y0, y1))))) MARK(cons1(cons(cons(y0, y1), y2), z1)) -> c10(MARK(cons(cons(y0, y1), y2))) MARK(cons1(cons(s(y0), y1), z1)) -> c10(MARK(cons(s(y0), y1))) MARK(cons1(cons(cons1(y0, y1), y2), z1)) -> c10(MARK(cons(cons1(y0, y1), y2))) MARK(cons1(cons(2nd(cons(y0, y1)), y2), z1)) -> c10(MARK(cons(2nd(cons(y0, y1)), y2))) MARK(cons1(cons(2nd(s(y0)), y1), z1)) -> c10(MARK(cons(2nd(s(y0)), y1))) MARK(cons1(cons(2nd(2nd(2nd(y0))), y1), z1)) -> c10(MARK(cons(2nd(2nd(2nd(y0))), y1))) MARK(cons1(cons(2nd(2nd(from(y0))), y1), z1)) -> c10(MARK(cons(2nd(2nd(from(y0))), y1))) MARK(cons1(cons(2nd(2nd(cons(y0, y1))), y2), z1)) -> c10(MARK(cons(2nd(2nd(cons(y0, y1))), y2))) MARK(cons1(cons(2nd(2nd(s(y0))), y1), z1)) -> c10(MARK(cons(2nd(2nd(s(y0))), y1))) MARK(cons1(cons(2nd(2nd(cons1(y0, y1))), y2), z1)) -> c10(MARK(cons(2nd(2nd(cons1(y0, y1))), y2))) MARK(cons1(cons(2nd(2nd(y0)), y1), z1)) -> c10(MARK(cons(2nd(2nd(y0)), y1))) MARK(cons1(cons(2nd(from(y0)), y1), z1)) -> c10(MARK(cons(2nd(from(y0)), y1))) MARK(cons1(cons(2nd(from(2nd(y0))), y1), z1)) -> c10(MARK(cons(2nd(from(2nd(y0))), y1))) MARK(cons1(cons(2nd(from(from(y0))), y1), z1)) -> c10(MARK(cons(2nd(from(from(y0))), y1))) MARK(cons1(cons(2nd(from(cons(y0, y1))), y2), z1)) -> c10(MARK(cons(2nd(from(cons(y0, y1))), y2))) MARK(cons1(cons(2nd(from(s(y0))), y1), z1)) -> c10(MARK(cons(2nd(from(s(y0))), y1))) MARK(cons1(cons(2nd(from(cons1(y0, y1))), y2), z1)) -> c10(MARK(cons(2nd(from(cons1(y0, y1))), y2))) MARK(cons1(cons(2nd(cons1(y0, 2nd(y1))), y2), z1)) -> c10(MARK(cons(2nd(cons1(y0, 2nd(y1))), y2))) MARK(cons1(cons(2nd(cons1(y0, from(y1))), y2), z1)) -> c10(MARK(cons(2nd(cons1(y0, from(y1))), y2))) MARK(cons1(cons(2nd(cons1(y0, cons(y1, y2))), y3), z1)) -> c10(MARK(cons(2nd(cons1(y0, cons(y1, y2))), y3))) MARK(cons1(cons(2nd(cons1(2nd(y0), y1)), y2), z1)) -> c10(MARK(cons(2nd(cons1(2nd(y0), y1)), y2))) MARK(cons1(cons(2nd(cons1(from(y0), y1)), y2), z1)) -> c10(MARK(cons(2nd(cons1(from(y0), y1)), y2))) MARK(cons1(cons(2nd(cons1(cons(y0, y1), y2)), y3), z1)) -> c10(MARK(cons(2nd(cons1(cons(y0, y1), y2)), y3))) MARK(cons1(cons(2nd(cons1(s(y0), y1)), y2), z1)) -> c10(MARK(cons(2nd(cons1(s(y0), y1)), y2))) MARK(cons1(cons(2nd(cons1(cons1(y0, y1), y2)), y3), z1)) -> c10(MARK(cons(2nd(cons1(cons1(y0, y1), y2)), y3))) MARK(cons1(cons(2nd(cons1(y0, y1)), y2), z1)) -> c10(MARK(cons(2nd(cons1(y0, y1)), y2))) MARK(cons1(cons(2nd(cons1(y0, s(y1))), y2), z1)) -> c10(MARK(cons(2nd(cons1(y0, s(y1))), y2))) MARK(cons1(cons(2nd(cons1(y0, cons1(y1, y2))), y3), z1)) -> c10(MARK(cons(2nd(cons1(y0, cons1(y1, y2))), y3))) MARK(cons1(cons(from(cons(y0, y1)), y2), z1)) -> c10(MARK(cons(from(cons(y0, y1)), y2))) MARK(cons1(cons(from(s(y0)), y1), z1)) -> c10(MARK(cons(from(s(y0)), y1))) MARK(cons1(cons(from(cons1(y0, y1)), y2), z1)) -> c10(MARK(cons(from(cons1(y0, y1)), y2))) MARK(cons1(cons(from(2nd(y0)), y1), z1)) -> c10(MARK(cons(from(2nd(y0)), y1))) MARK(cons1(cons(from(2nd(2nd(y0))), y1), z1)) -> c10(MARK(cons(from(2nd(2nd(y0))), y1))) MARK(cons1(cons(from(2nd(from(y0))), y1), z1)) -> c10(MARK(cons(from(2nd(from(y0))), y1))) MARK(cons1(cons(from(2nd(cons(y0, y1))), y2), z1)) -> c10(MARK(cons(from(2nd(cons(y0, y1))), y2))) MARK(cons1(cons(from(2nd(s(y0))), y1), z1)) -> c10(MARK(cons(from(2nd(s(y0))), y1))) MARK(cons1(cons(from(2nd(cons1(y0, y1))), y2), z1)) -> c10(MARK(cons(from(2nd(cons1(y0, y1))), y2))) MARK(cons1(cons(from(from(y0)), y1), z1)) -> c10(MARK(cons(from(from(y0)), y1))) MARK(cons1(cons(from(from(2nd(y0))), y1), z1)) -> c10(MARK(cons(from(from(2nd(y0))), y1))) MARK(cons1(cons(from(from(from(y0))), y1), z1)) -> c10(MARK(cons(from(from(from(y0))), y1))) MARK(cons1(cons(from(from(cons(y0, y1))), y2), z1)) -> c10(MARK(cons(from(from(cons(y0, y1))), y2))) MARK(cons1(cons(from(from(s(y0))), y1), z1)) -> c10(MARK(cons(from(from(s(y0))), y1))) MARK(cons1(cons(from(from(cons1(y0, y1))), y2), z1)) -> c10(MARK(cons(from(from(cons1(y0, y1))), y2))) MARK(cons1(s(s(y0)), z1)) -> c10(MARK(s(s(y0)))) MARK(cons1(s(cons1(y0, y1)), z1)) -> c10(MARK(s(cons1(y0, y1)))) MARK(cons1(s(2nd(cons(y0, y1))), z1)) -> c10(MARK(s(2nd(cons(y0, y1))))) MARK(cons1(s(2nd(s(y0))), z1)) -> c10(MARK(s(2nd(s(y0))))) MARK(cons1(s(2nd(2nd(2nd(y0)))), z1)) -> c10(MARK(s(2nd(2nd(2nd(y0)))))) MARK(cons1(s(2nd(2nd(from(y0)))), z1)) -> c10(MARK(s(2nd(2nd(from(y0)))))) MARK(cons1(s(2nd(2nd(cons(y0, y1)))), z1)) -> c10(MARK(s(2nd(2nd(cons(y0, y1)))))) MARK(cons1(s(2nd(2nd(s(y0)))), z1)) -> c10(MARK(s(2nd(2nd(s(y0)))))) MARK(cons1(s(2nd(2nd(cons1(y0, y1)))), z1)) -> c10(MARK(s(2nd(2nd(cons1(y0, y1)))))) MARK(cons1(s(2nd(2nd(y0))), z1)) -> c10(MARK(s(2nd(2nd(y0))))) MARK(cons1(s(2nd(from(y0))), z1)) -> c10(MARK(s(2nd(from(y0))))) MARK(cons1(s(2nd(from(2nd(y0)))), z1)) -> c10(MARK(s(2nd(from(2nd(y0)))))) MARK(cons1(s(2nd(from(from(y0)))), z1)) -> c10(MARK(s(2nd(from(from(y0)))))) MARK(cons1(s(2nd(from(cons(y0, y1)))), z1)) -> c10(MARK(s(2nd(from(cons(y0, y1)))))) MARK(cons1(s(2nd(from(s(y0)))), z1)) -> c10(MARK(s(2nd(from(s(y0)))))) MARK(cons1(s(2nd(from(cons1(y0, y1)))), z1)) -> c10(MARK(s(2nd(from(cons1(y0, y1)))))) MARK(cons1(s(2nd(cons1(y0, 2nd(y1)))), z1)) -> c10(MARK(s(2nd(cons1(y0, 2nd(y1)))))) MARK(cons1(s(2nd(cons1(y0, from(y1)))), z1)) -> c10(MARK(s(2nd(cons1(y0, from(y1)))))) MARK(cons1(s(2nd(cons1(y0, cons(y1, y2)))), z1)) -> c10(MARK(s(2nd(cons1(y0, cons(y1, y2)))))) MARK(cons1(s(2nd(cons1(2nd(y0), y1))), z1)) -> c10(MARK(s(2nd(cons1(2nd(y0), y1))))) MARK(cons1(s(2nd(cons1(from(y0), y1))), z1)) -> c10(MARK(s(2nd(cons1(from(y0), y1))))) MARK(cons1(s(2nd(cons1(cons(y0, y1), y2))), z1)) -> c10(MARK(s(2nd(cons1(cons(y0, y1), y2))))) MARK(cons1(s(2nd(cons1(s(y0), y1))), z1)) -> c10(MARK(s(2nd(cons1(s(y0), y1))))) MARK(cons1(s(2nd(cons1(cons1(y0, y1), y2))), z1)) -> c10(MARK(s(2nd(cons1(cons1(y0, y1), y2))))) MARK(cons1(s(2nd(cons1(y0, y1))), z1)) -> c10(MARK(s(2nd(cons1(y0, y1))))) MARK(cons1(s(2nd(cons1(y0, s(y1)))), z1)) -> c10(MARK(s(2nd(cons1(y0, s(y1)))))) MARK(cons1(s(2nd(cons1(y0, cons1(y1, y2)))), z1)) -> c10(MARK(s(2nd(cons1(y0, cons1(y1, y2)))))) MARK(cons1(s(from(cons(y0, y1))), z1)) -> c10(MARK(s(from(cons(y0, y1))))) MARK(cons1(s(from(s(y0))), z1)) -> c10(MARK(s(from(s(y0))))) MARK(cons1(s(from(cons1(y0, y1))), z1)) -> c10(MARK(s(from(cons1(y0, y1))))) MARK(cons1(s(from(2nd(y0))), z1)) -> c10(MARK(s(from(2nd(y0))))) MARK(cons1(s(from(2nd(2nd(y0)))), z1)) -> c10(MARK(s(from(2nd(2nd(y0)))))) MARK(cons1(s(from(2nd(from(y0)))), z1)) -> c10(MARK(s(from(2nd(from(y0)))))) MARK(cons1(s(from(2nd(cons(y0, y1)))), z1)) -> c10(MARK(s(from(2nd(cons(y0, y1)))))) MARK(cons1(s(from(2nd(s(y0)))), z1)) -> c10(MARK(s(from(2nd(s(y0)))))) MARK(cons1(s(from(2nd(cons1(y0, y1)))), z1)) -> c10(MARK(s(from(2nd(cons1(y0, y1)))))) MARK(cons1(s(from(from(y0))), z1)) -> c10(MARK(s(from(from(y0))))) MARK(cons1(s(from(from(2nd(y0)))), z1)) -> c10(MARK(s(from(from(2nd(y0)))))) MARK(cons1(s(from(from(from(y0)))), z1)) -> c10(MARK(s(from(from(from(y0)))))) MARK(cons1(s(from(from(cons(y0, y1)))), z1)) -> c10(MARK(s(from(from(cons(y0, y1)))))) MARK(cons1(s(from(from(s(y0)))), z1)) -> c10(MARK(s(from(from(s(y0)))))) MARK(cons1(s(from(from(cons1(y0, y1)))), z1)) -> c10(MARK(s(from(from(cons1(y0, y1)))))) MARK(cons1(s(cons(cons(y0, y1), y2)), z1)) -> c10(MARK(s(cons(cons(y0, y1), y2)))) MARK(cons1(s(cons(s(y0), y1)), z1)) -> c10(MARK(s(cons(s(y0), y1)))) MARK(cons1(s(cons(cons1(y0, y1), y2)), z1)) -> c10(MARK(s(cons(cons1(y0, y1), y2)))) MARK(cons1(s(cons(2nd(cons(y0, y1)), y2)), z1)) -> c10(MARK(s(cons(2nd(cons(y0, y1)), y2)))) MARK(cons1(s(cons(2nd(s(y0)), y1)), z1)) -> c10(MARK(s(cons(2nd(s(y0)), y1)))) MARK(cons1(s(cons(2nd(2nd(2nd(y0))), y1)), z1)) -> c10(MARK(s(cons(2nd(2nd(2nd(y0))), y1)))) MARK(cons1(s(cons(2nd(2nd(from(y0))), y1)), z1)) -> c10(MARK(s(cons(2nd(2nd(from(y0))), y1)))) MARK(cons1(s(cons(2nd(2nd(cons(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(2nd(cons(y0, y1))), y2)))) MARK(cons1(s(cons(2nd(2nd(s(y0))), y1)), z1)) -> 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c11(MARK(s(2nd(2nd(cons1(y0, y1)))))) MARK(cons1(z0, s(2nd(2nd(y0))))) -> c11(MARK(s(2nd(2nd(y0))))) MARK(cons1(z0, s(2nd(from(y0))))) -> c11(MARK(s(2nd(from(y0))))) MARK(cons1(z0, s(2nd(from(2nd(y0)))))) -> c11(MARK(s(2nd(from(2nd(y0)))))) MARK(cons1(z0, s(2nd(from(from(y0)))))) -> c11(MARK(s(2nd(from(from(y0)))))) MARK(cons1(z0, s(2nd(from(cons(y0, y1)))))) -> c11(MARK(s(2nd(from(cons(y0, y1)))))) MARK(cons1(z0, s(2nd(from(s(y0)))))) -> c11(MARK(s(2nd(from(s(y0)))))) MARK(cons1(z0, s(2nd(from(cons1(y0, y1)))))) -> c11(MARK(s(2nd(from(cons1(y0, y1)))))) MARK(cons1(z0, s(2nd(cons1(y0, 2nd(y1)))))) -> c11(MARK(s(2nd(cons1(y0, 2nd(y1)))))) MARK(cons1(z0, s(2nd(cons1(y0, from(y1)))))) -> c11(MARK(s(2nd(cons1(y0, from(y1)))))) MARK(cons1(z0, s(2nd(cons1(y0, cons(y1, y2)))))) -> c11(MARK(s(2nd(cons1(y0, cons(y1, y2)))))) MARK(cons1(z0, s(2nd(cons1(2nd(y0), y1))))) -> c11(MARK(s(2nd(cons1(2nd(y0), y1))))) MARK(cons1(z0, s(2nd(cons1(from(y0), y1))))) -> c11(MARK(s(2nd(cons1(from(y0), y1))))) MARK(cons1(z0, s(2nd(cons1(cons(y0, y1), y2))))) -> c11(MARK(s(2nd(cons1(cons(y0, y1), y2))))) MARK(cons1(z0, s(2nd(cons1(s(y0), y1))))) -> c11(MARK(s(2nd(cons1(s(y0), y1))))) MARK(cons1(z0, s(2nd(cons1(cons1(y0, y1), y2))))) -> c11(MARK(s(2nd(cons1(cons1(y0, y1), y2))))) MARK(cons1(z0, s(2nd(cons1(y0, y1))))) -> c11(MARK(s(2nd(cons1(y0, y1))))) MARK(cons1(z0, s(2nd(cons1(y0, s(y1)))))) -> c11(MARK(s(2nd(cons1(y0, s(y1)))))) MARK(cons1(z0, s(2nd(cons1(y0, cons1(y1, y2)))))) -> c11(MARK(s(2nd(cons1(y0, cons1(y1, y2)))))) MARK(cons1(z0, s(from(cons(y0, y1))))) -> c11(MARK(s(from(cons(y0, y1))))) MARK(cons1(z0, s(from(s(y0))))) -> c11(MARK(s(from(s(y0))))) MARK(cons1(z0, s(from(cons1(y0, y1))))) -> c11(MARK(s(from(cons1(y0, y1))))) MARK(cons1(z0, s(from(2nd(y0))))) -> c11(MARK(s(from(2nd(y0))))) MARK(cons1(z0, s(from(2nd(2nd(y0)))))) -> c11(MARK(s(from(2nd(2nd(y0)))))) MARK(cons1(z0, s(from(2nd(from(y0)))))) -> c11(MARK(s(from(2nd(from(y0)))))) MARK(cons1(z0, s(from(2nd(cons(y0, y1)))))) -> c11(MARK(s(from(2nd(cons(y0, y1)))))) MARK(cons1(z0, s(from(2nd(s(y0)))))) -> c11(MARK(s(from(2nd(s(y0)))))) MARK(cons1(z0, s(from(2nd(cons1(y0, y1)))))) -> c11(MARK(s(from(2nd(cons1(y0, y1)))))) MARK(cons1(z0, s(from(from(y0))))) -> c11(MARK(s(from(from(y0))))) MARK(cons1(z0, s(from(from(2nd(y0)))))) -> c11(MARK(s(from(from(2nd(y0)))))) MARK(cons1(z0, s(from(from(from(y0)))))) -> c11(MARK(s(from(from(from(y0)))))) MARK(cons1(z0, s(from(from(cons(y0, y1)))))) -> c11(MARK(s(from(from(cons(y0, y1)))))) MARK(cons1(z0, s(from(from(s(y0)))))) -> c11(MARK(s(from(from(s(y0)))))) MARK(cons1(z0, s(from(from(cons1(y0, y1)))))) -> c11(MARK(s(from(from(cons1(y0, y1)))))) MARK(cons1(z0, s(cons(cons(y0, y1), y2)))) -> c11(MARK(s(cons(cons(y0, y1), y2)))) MARK(cons1(z0, s(cons(s(y0), y1)))) -> c11(MARK(s(cons(s(y0), y1)))) MARK(cons1(z0, s(cons(cons1(y0, y1), y2)))) -> c11(MARK(s(cons(cons1(y0, y1), y2)))) MARK(cons1(z0, s(cons(2nd(cons(y0, y1)), y2)))) -> c11(MARK(s(cons(2nd(cons(y0, y1)), y2)))) MARK(cons1(z0, s(cons(2nd(s(y0)), y1)))) -> c11(MARK(s(cons(2nd(s(y0)), y1)))) MARK(cons1(z0, s(cons(2nd(2nd(2nd(y0))), y1)))) -> c11(MARK(s(cons(2nd(2nd(2nd(y0))), y1)))) MARK(cons1(z0, s(cons(2nd(2nd(from(y0))), y1)))) -> c11(MARK(s(cons(2nd(2nd(from(y0))), y1)))) MARK(cons1(z0, s(cons(2nd(2nd(cons(y0, y1))), y2)))) -> c11(MARK(s(cons(2nd(2nd(cons(y0, y1))), y2)))) MARK(cons1(z0, s(cons(2nd(2nd(s(y0))), y1)))) -> c11(MARK(s(cons(2nd(2nd(s(y0))), y1)))) MARK(cons1(z0, s(cons(2nd(2nd(cons1(y0, y1))), y2)))) -> c11(MARK(s(cons(2nd(2nd(cons1(y0, y1))), y2)))) MARK(cons1(z0, s(cons(2nd(2nd(y0)), y1)))) -> c11(MARK(s(cons(2nd(2nd(y0)), y1)))) MARK(cons1(z0, s(cons(2nd(from(y0)), y1)))) -> c11(MARK(s(cons(2nd(from(y0)), y1)))) MARK(cons1(z0, s(cons(2nd(from(2nd(y0))), y1)))) -> c11(MARK(s(cons(2nd(from(2nd(y0))), y1)))) MARK(cons1(z0, s(cons(2nd(from(from(y0))), y1)))) -> c11(MARK(s(cons(2nd(from(from(y0))), y1)))) MARK(cons1(z0, s(cons(2nd(from(cons(y0, y1))), y2)))) -> c11(MARK(s(cons(2nd(from(cons(y0, y1))), y2)))) MARK(cons1(z0, s(cons(2nd(from(s(y0))), y1)))) -> c11(MARK(s(cons(2nd(from(s(y0))), y1)))) MARK(cons1(z0, s(cons(2nd(from(cons1(y0, y1))), y2)))) -> c11(MARK(s(cons(2nd(from(cons1(y0, y1))), y2)))) MARK(cons1(z0, s(cons(2nd(cons1(y0, 2nd(y1))), y2)))) -> c11(MARK(s(cons(2nd(cons1(y0, 2nd(y1))), y2)))) MARK(cons1(z0, s(cons(2nd(cons1(y0, from(y1))), y2)))) -> c11(MARK(s(cons(2nd(cons1(y0, from(y1))), y2)))) MARK(cons1(z0, s(cons(2nd(cons1(y0, cons(y1, y2))), y3)))) -> c11(MARK(s(cons(2nd(cons1(y0, cons(y1, y2))), y3)))) MARK(cons1(z0, s(cons(2nd(cons1(2nd(y0), y1)), y2)))) -> c11(MARK(s(cons(2nd(cons1(2nd(y0), y1)), y2)))) MARK(cons1(z0, s(cons(2nd(cons1(from(y0), y1)), y2)))) -> c11(MARK(s(cons(2nd(cons1(from(y0), y1)), y2)))) MARK(cons1(z0, s(cons(2nd(cons1(cons(y0, y1), y2)), y3)))) -> c11(MARK(s(cons(2nd(cons1(cons(y0, y1), y2)), y3)))) MARK(cons1(z0, s(cons(2nd(cons1(s(y0), y1)), y2)))) -> c11(MARK(s(cons(2nd(cons1(s(y0), y1)), y2)))) MARK(cons1(z0, s(cons(2nd(cons1(cons1(y0, y1), y2)), y3)))) -> c11(MARK(s(cons(2nd(cons1(cons1(y0, y1), y2)), y3)))) MARK(cons1(z0, s(cons(2nd(cons1(y0, y1)), y2)))) -> c11(MARK(s(cons(2nd(cons1(y0, y1)), y2)))) MARK(cons1(z0, s(cons(2nd(cons1(y0, s(y1))), y2)))) -> c11(MARK(s(cons(2nd(cons1(y0, s(y1))), y2)))) MARK(cons1(z0, s(cons(2nd(cons1(y0, cons1(y1, y2))), y3)))) -> c11(MARK(s(cons(2nd(cons1(y0, cons1(y1, y2))), y3)))) MARK(cons1(z0, s(cons(from(cons(y0, y1)), y2)))) -> c11(MARK(s(cons(from(cons(y0, y1)), y2)))) MARK(cons1(z0, s(cons(from(s(y0)), y1)))) -> c11(MARK(s(cons(from(s(y0)), y1)))) MARK(cons1(z0, s(cons(from(cons1(y0, y1)), y2)))) -> c11(MARK(s(cons(from(cons1(y0, y1)), y2)))) MARK(cons1(z0, s(cons(from(2nd(y0)), y1)))) -> c11(MARK(s(cons(from(2nd(y0)), y1)))) MARK(cons1(z0, s(cons(from(2nd(2nd(y0))), y1)))) -> c11(MARK(s(cons(from(2nd(2nd(y0))), y1)))) MARK(cons1(z0, s(cons(from(2nd(from(y0))), y1)))) -> c11(MARK(s(cons(from(2nd(from(y0))), y1)))) MARK(cons1(z0, s(cons(from(2nd(cons(y0, y1))), y2)))) -> c11(MARK(s(cons(from(2nd(cons(y0, y1))), y2)))) MARK(cons1(z0, s(cons(from(2nd(s(y0))), y1)))) -> c11(MARK(s(cons(from(2nd(s(y0))), y1)))) MARK(cons1(z0, s(cons(from(2nd(cons1(y0, y1))), y2)))) -> c11(MARK(s(cons(from(2nd(cons1(y0, y1))), y2)))) MARK(cons1(z0, s(cons(from(from(y0)), y1)))) -> c11(MARK(s(cons(from(from(y0)), y1)))) MARK(cons1(z0, s(cons(from(from(2nd(y0))), y1)))) -> c11(MARK(s(cons(from(from(2nd(y0))), y1)))) MARK(cons1(z0, s(cons(from(from(from(y0))), y1)))) -> c11(MARK(s(cons(from(from(from(y0))), y1)))) MARK(cons1(z0, s(cons(from(from(cons(y0, y1))), y2)))) -> c11(MARK(s(cons(from(from(cons(y0, y1))), y2)))) MARK(cons1(z0, s(cons(from(from(s(y0))), y1)))) -> c11(MARK(s(cons(from(from(s(y0))), y1)))) MARK(cons1(z0, s(cons(from(from(cons1(y0, y1))), y2)))) -> c11(MARK(s(cons(from(from(cons1(y0, y1))), y2)))) MARK(cons1(z0, cons1(cons1(y0, y1), y2))) -> c11(MARK(cons1(cons1(y0, y1), y2))) MARK(cons1(z0, cons1(2nd(cons(y0, y1)), y2))) -> c11(MARK(cons1(2nd(cons(y0, y1)), y2))) MARK(cons1(z0, cons1(2nd(s(y0)), y1))) -> c11(MARK(cons1(2nd(s(y0)), y1))) MARK(cons1(z0, cons1(2nd(2nd(2nd(y0))), y1))) -> c11(MARK(cons1(2nd(2nd(2nd(y0))), y1))) MARK(cons1(z0, cons1(2nd(2nd(from(y0))), y1))) -> c11(MARK(cons1(2nd(2nd(from(y0))), y1))) MARK(cons1(z0, cons1(2nd(2nd(cons(y0, y1))), y2))) -> c11(MARK(cons1(2nd(2nd(cons(y0, y1))), y2))) MARK(cons1(z0, cons1(2nd(2nd(s(y0))), y1))) -> c11(MARK(cons1(2nd(2nd(s(y0))), y1))) MARK(cons1(z0, cons1(2nd(2nd(cons1(y0, y1))), y2))) -> c11(MARK(cons1(2nd(2nd(cons1(y0, y1))), y2))) MARK(cons1(z0, cons1(2nd(2nd(y0)), y1))) -> c11(MARK(cons1(2nd(2nd(y0)), y1))) MARK(cons1(z0, cons1(2nd(from(y0)), y1))) -> c11(MARK(cons1(2nd(from(y0)), y1))) MARK(cons1(z0, cons1(2nd(from(2nd(y0))), y1))) -> c11(MARK(cons1(2nd(from(2nd(y0))), y1))) MARK(cons1(z0, cons1(2nd(from(from(y0))), y1))) -> c11(MARK(cons1(2nd(from(from(y0))), y1))) MARK(cons1(z0, cons1(2nd(from(cons(y0, y1))), y2))) -> c11(MARK(cons1(2nd(from(cons(y0, y1))), y2))) MARK(cons1(z0, cons1(2nd(from(s(y0))), y1))) -> c11(MARK(cons1(2nd(from(s(y0))), y1))) MARK(cons1(z0, cons1(2nd(from(cons1(y0, y1))), y2))) -> c11(MARK(cons1(2nd(from(cons1(y0, y1))), y2))) MARK(cons1(z0, cons1(2nd(cons1(y0, 2nd(y1))), y2))) -> c11(MARK(cons1(2nd(cons1(y0, 2nd(y1))), y2))) MARK(cons1(z0, cons1(2nd(cons1(y0, from(y1))), y2))) -> c11(MARK(cons1(2nd(cons1(y0, from(y1))), y2))) MARK(cons1(z0, cons1(2nd(cons1(y0, cons(y1, y2))), y3))) -> c11(MARK(cons1(2nd(cons1(y0, cons(y1, y2))), y3))) MARK(cons1(z0, cons1(2nd(cons1(2nd(y0), y1)), y2))) -> c11(MARK(cons1(2nd(cons1(2nd(y0), y1)), y2))) MARK(cons1(z0, cons1(2nd(cons1(from(y0), y1)), y2))) -> c11(MARK(cons1(2nd(cons1(from(y0), y1)), y2))) MARK(cons1(z0, cons1(2nd(cons1(cons(y0, y1), y2)), y3))) -> c11(MARK(cons1(2nd(cons1(cons(y0, y1), y2)), y3))) MARK(cons1(z0, cons1(2nd(cons1(s(y0), y1)), y2))) -> c11(MARK(cons1(2nd(cons1(s(y0), y1)), y2))) MARK(cons1(z0, cons1(2nd(cons1(cons1(y0, y1), y2)), y3))) -> c11(MARK(cons1(2nd(cons1(cons1(y0, y1), y2)), y3))) MARK(cons1(z0, cons1(2nd(cons1(y0, y1)), y2))) -> c11(MARK(cons1(2nd(cons1(y0, y1)), y2))) MARK(cons1(z0, cons1(2nd(cons1(y0, s(y1))), y2))) -> c11(MARK(cons1(2nd(cons1(y0, s(y1))), y2))) MARK(cons1(z0, cons1(2nd(cons1(y0, cons1(y1, y2))), y3))) -> c11(MARK(cons1(2nd(cons1(y0, cons1(y1, y2))), y3))) MARK(cons1(z0, cons1(from(cons(y0, y1)), y2))) -> c11(MARK(cons1(from(cons(y0, y1)), y2))) MARK(cons1(z0, cons1(from(s(y0)), y1))) -> c11(MARK(cons1(from(s(y0)), y1))) MARK(cons1(z0, cons1(from(cons1(y0, y1)), y2))) -> c11(MARK(cons1(from(cons1(y0, y1)), y2))) MARK(cons1(z0, cons1(from(2nd(y0)), y1))) -> c11(MARK(cons1(from(2nd(y0)), y1))) MARK(cons1(z0, cons1(from(2nd(2nd(y0))), y1))) -> c11(MARK(cons1(from(2nd(2nd(y0))), y1))) MARK(cons1(z0, cons1(from(2nd(from(y0))), y1))) -> c11(MARK(cons1(from(2nd(from(y0))), y1))) MARK(cons1(z0, cons1(from(2nd(cons(y0, y1))), y2))) -> c11(MARK(cons1(from(2nd(cons(y0, y1))), y2))) MARK(cons1(z0, cons1(from(2nd(s(y0))), y1))) -> c11(MARK(cons1(from(2nd(s(y0))), y1))) MARK(cons1(z0, cons1(from(2nd(cons1(y0, y1))), y2))) -> c11(MARK(cons1(from(2nd(cons1(y0, y1))), y2))) MARK(cons1(z0, cons1(from(from(y0)), y1))) -> c11(MARK(cons1(from(from(y0)), y1))) MARK(cons1(z0, cons1(from(from(2nd(y0))), y1))) -> c11(MARK(cons1(from(from(2nd(y0))), y1))) MARK(cons1(z0, cons1(from(from(from(y0))), y1))) -> c11(MARK(cons1(from(from(from(y0))), y1))) MARK(cons1(z0, cons1(from(from(cons(y0, y1))), y2))) -> c11(MARK(cons1(from(from(cons(y0, y1))), y2))) MARK(cons1(z0, cons1(from(from(s(y0))), y1))) -> c11(MARK(cons1(from(from(s(y0))), y1))) MARK(cons1(z0, cons1(from(from(cons1(y0, y1))), y2))) -> c11(MARK(cons1(from(from(cons1(y0, y1))), y2))) MARK(cons1(z0, cons1(cons(cons(y0, y1), y2), y3))) -> c11(MARK(cons1(cons(cons(y0, y1), y2), y3))) MARK(cons1(z0, cons1(cons(s(y0), y1), y2))) -> c11(MARK(cons1(cons(s(y0), y1), y2))) MARK(cons1(z0, cons1(cons(cons1(y0, y1), y2), y3))) -> c11(MARK(cons1(cons(cons1(y0, y1), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(cons(y0, y1)), y2), y3))) -> c11(MARK(cons1(cons(2nd(cons(y0, y1)), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(s(y0)), y1), y2))) -> c11(MARK(cons1(cons(2nd(s(y0)), y1), y2))) MARK(cons1(z0, cons1(cons(2nd(2nd(2nd(y0))), y1), y2))) -> c11(MARK(cons1(cons(2nd(2nd(2nd(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(2nd(2nd(from(y0))), y1), y2))) -> c11(MARK(cons1(cons(2nd(2nd(from(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(2nd(2nd(cons(y0, y1))), y2), y3))) -> c11(MARK(cons1(cons(2nd(2nd(cons(y0, y1))), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(2nd(s(y0))), y1), y2))) -> c11(MARK(cons1(cons(2nd(2nd(s(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(2nd(2nd(cons1(y0, y1))), y2), y3))) -> c11(MARK(cons1(cons(2nd(2nd(cons1(y0, y1))), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(2nd(y0)), y1), y2))) -> c11(MARK(cons1(cons(2nd(2nd(y0)), y1), y2))) MARK(cons1(z0, cons1(cons(2nd(from(y0)), y1), y2))) -> c11(MARK(cons1(cons(2nd(from(y0)), y1), y2))) MARK(cons1(z0, cons1(cons(2nd(from(2nd(y0))), y1), y2))) -> c11(MARK(cons1(cons(2nd(from(2nd(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(2nd(from(from(y0))), y1), y2))) -> c11(MARK(cons1(cons(2nd(from(from(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(2nd(from(cons(y0, y1))), y2), y3))) -> c11(MARK(cons1(cons(2nd(from(cons(y0, y1))), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(from(s(y0))), y1), y2))) -> c11(MARK(cons1(cons(2nd(from(s(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(2nd(from(cons1(y0, y1))), y2), y3))) -> c11(MARK(cons1(cons(2nd(from(cons1(y0, y1))), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(cons1(y0, 2nd(y1))), y2), y3))) -> c11(MARK(cons1(cons(2nd(cons1(y0, 2nd(y1))), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(cons1(y0, from(y1))), y2), y3))) -> c11(MARK(cons1(cons(2nd(cons1(y0, from(y1))), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(cons1(y0, cons(y1, y2))), y3), y4))) -> c11(MARK(cons1(cons(2nd(cons1(y0, cons(y1, y2))), y3), y4))) MARK(cons1(z0, cons1(cons(2nd(cons1(2nd(y0), y1)), y2), y3))) -> c11(MARK(cons1(cons(2nd(cons1(2nd(y0), y1)), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(cons1(from(y0), y1)), y2), y3))) -> c11(MARK(cons1(cons(2nd(cons1(from(y0), y1)), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(cons1(cons(y0, y1), y2)), y3), y4))) -> c11(MARK(cons1(cons(2nd(cons1(cons(y0, y1), y2)), y3), y4))) MARK(cons1(z0, cons1(cons(2nd(cons1(s(y0), y1)), y2), y3))) -> c11(MARK(cons1(cons(2nd(cons1(s(y0), y1)), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(cons1(cons1(y0, y1), y2)), y3), y4))) -> c11(MARK(cons1(cons(2nd(cons1(cons1(y0, y1), y2)), y3), y4))) MARK(cons1(z0, cons1(cons(2nd(cons1(y0, y1)), y2), y3))) -> c11(MARK(cons1(cons(2nd(cons1(y0, y1)), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(cons1(y0, s(y1))), y2), y3))) -> c11(MARK(cons1(cons(2nd(cons1(y0, s(y1))), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(cons1(y0, cons1(y1, y2))), y3), y4))) -> c11(MARK(cons1(cons(2nd(cons1(y0, cons1(y1, y2))), y3), y4))) MARK(cons1(z0, cons1(cons(from(cons(y0, y1)), y2), y3))) -> c11(MARK(cons1(cons(from(cons(y0, y1)), y2), y3))) MARK(cons1(z0, cons1(cons(from(s(y0)), y1), y2))) -> c11(MARK(cons1(cons(from(s(y0)), y1), y2))) MARK(cons1(z0, cons1(cons(from(cons1(y0, y1)), y2), y3))) -> c11(MARK(cons1(cons(from(cons1(y0, y1)), y2), y3))) MARK(cons1(z0, cons1(cons(from(2nd(y0)), y1), y2))) -> c11(MARK(cons1(cons(from(2nd(y0)), y1), y2))) MARK(cons1(z0, cons1(cons(from(2nd(2nd(y0))), y1), y2))) -> c11(MARK(cons1(cons(from(2nd(2nd(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(from(2nd(from(y0))), y1), y2))) -> c11(MARK(cons1(cons(from(2nd(from(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(from(2nd(cons(y0, y1))), y2), y3))) -> c11(MARK(cons1(cons(from(2nd(cons(y0, y1))), y2), y3))) MARK(cons1(z0, cons1(cons(from(2nd(s(y0))), y1), y2))) -> c11(MARK(cons1(cons(from(2nd(s(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(from(2nd(cons1(y0, y1))), y2), y3))) -> c11(MARK(cons1(cons(from(2nd(cons1(y0, y1))), y2), y3))) MARK(cons1(z0, cons1(cons(from(from(y0)), y1), y2))) -> c11(MARK(cons1(cons(from(from(y0)), y1), y2))) MARK(cons1(z0, cons1(cons(from(from(2nd(y0))), y1), y2))) -> c11(MARK(cons1(cons(from(from(2nd(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(from(from(from(y0))), y1), y2))) -> c11(MARK(cons1(cons(from(from(from(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(from(from(cons(y0, y1))), y2), y3))) -> c11(MARK(cons1(cons(from(from(cons(y0, y1))), y2), y3))) MARK(cons1(z0, cons1(cons(from(from(s(y0))), y1), y2))) -> c11(MARK(cons1(cons(from(from(s(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(from(from(cons1(y0, y1))), y2), y3))) -> c11(MARK(cons1(cons(from(from(cons1(y0, y1))), y2), y3))) MARK(cons1(z0, cons1(s(s(y0)), y1))) -> c11(MARK(cons1(s(s(y0)), y1))) MARK(cons1(z0, cons1(s(cons1(y0, y1)), y2))) -> c11(MARK(cons1(s(cons1(y0, y1)), y2))) MARK(cons1(z0, cons1(s(2nd(cons(y0, y1))), y2))) -> c11(MARK(cons1(s(2nd(cons(y0, y1))), y2))) MARK(cons1(z0, cons1(s(2nd(s(y0))), y1))) -> c11(MARK(cons1(s(2nd(s(y0))), y1))) MARK(cons1(z0, cons1(s(2nd(2nd(2nd(y0)))), y1))) -> c11(MARK(cons1(s(2nd(2nd(2nd(y0)))), y1))) MARK(cons1(z0, cons1(s(2nd(2nd(from(y0)))), y1))) -> c11(MARK(cons1(s(2nd(2nd(from(y0)))), y1))) MARK(cons1(z0, cons1(s(2nd(2nd(cons(y0, y1)))), y2))) -> c11(MARK(cons1(s(2nd(2nd(cons(y0, y1)))), y2))) MARK(cons1(z0, cons1(s(2nd(2nd(s(y0)))), y1))) -> c11(MARK(cons1(s(2nd(2nd(s(y0)))), y1))) MARK(cons1(z0, cons1(s(2nd(2nd(cons1(y0, y1)))), y2))) -> c11(MARK(cons1(s(2nd(2nd(cons1(y0, y1)))), y2))) MARK(cons1(z0, cons1(s(2nd(2nd(y0))), y1))) -> c11(MARK(cons1(s(2nd(2nd(y0))), y1))) MARK(cons1(z0, cons1(s(2nd(from(y0))), y1))) -> c11(MARK(cons1(s(2nd(from(y0))), y1))) MARK(cons1(z0, cons1(s(2nd(from(2nd(y0)))), y1))) -> c11(MARK(cons1(s(2nd(from(2nd(y0)))), y1))) MARK(cons1(z0, cons1(s(2nd(from(from(y0)))), y1))) -> c11(MARK(cons1(s(2nd(from(from(y0)))), y1))) MARK(cons1(z0, cons1(s(2nd(from(cons(y0, y1)))), y2))) -> c11(MARK(cons1(s(2nd(from(cons(y0, y1)))), y2))) MARK(cons1(z0, cons1(s(2nd(from(s(y0)))), y1))) -> c11(MARK(cons1(s(2nd(from(s(y0)))), y1))) MARK(cons1(z0, cons1(s(2nd(from(cons1(y0, y1)))), y2))) -> c11(MARK(cons1(s(2nd(from(cons1(y0, y1)))), y2))) MARK(cons1(z0, cons1(s(2nd(cons1(y0, 2nd(y1)))), y2))) -> c11(MARK(cons1(s(2nd(cons1(y0, 2nd(y1)))), y2))) MARK(cons1(z0, cons1(s(2nd(cons1(y0, from(y1)))), y2))) -> c11(MARK(cons1(s(2nd(cons1(y0, from(y1)))), y2))) MARK(cons1(z0, cons1(s(2nd(cons1(y0, cons(y1, y2)))), y3))) -> c11(MARK(cons1(s(2nd(cons1(y0, cons(y1, y2)))), y3))) MARK(cons1(z0, cons1(s(2nd(cons1(2nd(y0), y1))), y2))) -> c11(MARK(cons1(s(2nd(cons1(2nd(y0), y1))), y2))) MARK(cons1(z0, cons1(s(2nd(cons1(from(y0), y1))), y2))) -> c11(MARK(cons1(s(2nd(cons1(from(y0), y1))), y2))) MARK(cons1(z0, cons1(s(2nd(cons1(cons(y0, y1), y2))), y3))) -> c11(MARK(cons1(s(2nd(cons1(cons(y0, y1), y2))), y3))) MARK(cons1(z0, cons1(s(2nd(cons1(s(y0), y1))), y2))) -> c11(MARK(cons1(s(2nd(cons1(s(y0), y1))), y2))) MARK(cons1(z0, cons1(s(2nd(cons1(cons1(y0, y1), y2))), y3))) -> c11(MARK(cons1(s(2nd(cons1(cons1(y0, y1), y2))), y3))) MARK(cons1(z0, cons1(s(2nd(cons1(y0, y1))), y2))) -> c11(MARK(cons1(s(2nd(cons1(y0, y1))), y2))) MARK(cons1(z0, cons1(s(2nd(cons1(y0, s(y1)))), y2))) -> c11(MARK(cons1(s(2nd(cons1(y0, s(y1)))), y2))) MARK(cons1(z0, cons1(s(2nd(cons1(y0, cons1(y1, y2)))), y3))) -> c11(MARK(cons1(s(2nd(cons1(y0, cons1(y1, y2)))), y3))) MARK(cons1(z0, cons1(s(from(cons(y0, y1))), y2))) -> c11(MARK(cons1(s(from(cons(y0, y1))), y2))) MARK(cons1(z0, cons1(s(from(s(y0))), y1))) -> c11(MARK(cons1(s(from(s(y0))), y1))) MARK(cons1(z0, cons1(s(from(cons1(y0, y1))), y2))) -> c11(MARK(cons1(s(from(cons1(y0, y1))), y2))) MARK(cons1(z0, cons1(s(from(2nd(y0))), y1))) -> c11(MARK(cons1(s(from(2nd(y0))), y1))) MARK(cons1(z0, cons1(s(from(2nd(2nd(y0)))), y1))) -> c11(MARK(cons1(s(from(2nd(2nd(y0)))), y1))) MARK(cons1(z0, cons1(s(from(2nd(from(y0)))), y1))) -> c11(MARK(cons1(s(from(2nd(from(y0)))), y1))) MARK(cons1(z0, cons1(s(from(2nd(cons(y0, y1)))), y2))) -> c11(MARK(cons1(s(from(2nd(cons(y0, y1)))), y2))) MARK(cons1(z0, cons1(s(from(2nd(s(y0)))), y1))) -> c11(MARK(cons1(s(from(2nd(s(y0)))), y1))) MARK(cons1(z0, cons1(s(from(2nd(cons1(y0, y1)))), y2))) -> c11(MARK(cons1(s(from(2nd(cons1(y0, y1)))), y2))) MARK(cons1(z0, cons1(s(from(from(y0))), y1))) -> c11(MARK(cons1(s(from(from(y0))), y1))) MARK(cons1(z0, cons1(s(from(from(2nd(y0)))), y1))) -> c11(MARK(cons1(s(from(from(2nd(y0)))), y1))) MARK(cons1(z0, cons1(s(from(from(from(y0)))), y1))) -> c11(MARK(cons1(s(from(from(from(y0)))), y1))) MARK(cons1(z0, cons1(s(from(from(cons(y0, y1)))), y2))) -> c11(MARK(cons1(s(from(from(cons(y0, y1)))), y2))) MARK(cons1(z0, cons1(s(from(from(s(y0)))), y1))) -> c11(MARK(cons1(s(from(from(s(y0)))), y1))) MARK(cons1(z0, cons1(s(from(from(cons1(y0, y1)))), y2))) -> c11(MARK(cons1(s(from(from(cons1(y0, y1)))), y2))) MARK(cons1(z0, cons1(s(cons(cons(y0, y1), y2)), y3))) -> c11(MARK(cons1(s(cons(cons(y0, y1), y2)), y3))) MARK(cons1(z0, cons1(s(cons(s(y0), y1)), y2))) -> c11(MARK(cons1(s(cons(s(y0), y1)), y2))) MARK(cons1(z0, cons1(s(cons(cons1(y0, y1), y2)), y3))) -> c11(MARK(cons1(s(cons(cons1(y0, y1), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(cons(y0, y1)), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(cons(y0, y1)), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(s(y0)), y1)), y2))) -> c11(MARK(cons1(s(cons(2nd(s(y0)), y1)), y2))) MARK(cons1(z0, cons1(s(cons(2nd(2nd(2nd(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(2nd(2nd(2nd(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(2nd(2nd(from(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(2nd(2nd(from(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(2nd(2nd(cons(y0, y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(2nd(cons(y0, y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(2nd(s(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(2nd(2nd(s(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(2nd(2nd(cons1(y0, y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(2nd(cons1(y0, y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(2nd(y0)), y1)), y2))) -> c11(MARK(cons1(s(cons(2nd(2nd(y0)), y1)), y2))) MARK(cons1(z0, cons1(s(cons(2nd(from(y0)), y1)), y2))) -> c11(MARK(cons1(s(cons(2nd(from(y0)), y1)), y2))) MARK(cons1(z0, cons1(s(cons(2nd(from(2nd(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(2nd(from(2nd(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(2nd(from(from(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(2nd(from(from(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(2nd(from(cons(y0, y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(from(cons(y0, y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(from(s(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(2nd(from(s(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(2nd(from(cons1(y0, y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(from(cons1(y0, y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(y0, 2nd(y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(cons1(y0, 2nd(y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(y0, from(y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(cons1(y0, from(y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(y0, cons(y1, y2))), y3)), y4))) -> c11(MARK(cons1(s(cons(2nd(cons1(y0, cons(y1, y2))), y3)), y4))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(2nd(y0), y1)), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(cons1(2nd(y0), y1)), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(from(y0), y1)), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(cons1(from(y0), y1)), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(cons(y0, y1), y2)), y3)), y4))) -> c11(MARK(cons1(s(cons(2nd(cons1(cons(y0, y1), y2)), y3)), y4))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(s(y0), y1)), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(cons1(s(y0), y1)), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(cons1(y0, y1), y2)), y3)), y4))) -> c11(MARK(cons1(s(cons(2nd(cons1(cons1(y0, y1), y2)), y3)), y4))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(y0, y1)), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(cons1(y0, y1)), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(y0, s(y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(cons1(y0, s(y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(y0, cons1(y1, y2))), y3)), y4))) -> c11(MARK(cons1(s(cons(2nd(cons1(y0, cons1(y1, y2))), y3)), y4))) MARK(cons1(z0, cons1(s(cons(from(cons(y0, y1)), y2)), y3))) -> c11(MARK(cons1(s(cons(from(cons(y0, y1)), y2)), y3))) MARK(cons1(z0, cons1(s(cons(from(s(y0)), y1)), y2))) -> c11(MARK(cons1(s(cons(from(s(y0)), y1)), y2))) MARK(cons1(z0, cons1(s(cons(from(cons1(y0, y1)), y2)), y3))) -> c11(MARK(cons1(s(cons(from(cons1(y0, y1)), y2)), y3))) MARK(cons1(z0, cons1(s(cons(from(2nd(y0)), y1)), y2))) -> c11(MARK(cons1(s(cons(from(2nd(y0)), y1)), y2))) MARK(cons1(z0, cons1(s(cons(from(2nd(2nd(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(from(2nd(2nd(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(from(2nd(from(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(from(2nd(from(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(from(2nd(cons(y0, y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(from(2nd(cons(y0, y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(from(2nd(s(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(from(2nd(s(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(from(2nd(cons1(y0, y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(from(2nd(cons1(y0, y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(from(from(y0)), y1)), y2))) -> c11(MARK(cons1(s(cons(from(from(y0)), y1)), y2))) MARK(cons1(z0, cons1(s(cons(from(from(2nd(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(from(from(2nd(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(from(from(from(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(from(from(from(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(from(from(cons(y0, y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(from(from(cons(y0, y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(from(from(s(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(from(from(s(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(from(from(cons1(y0, y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(from(from(cons1(y0, y1))), y2)), y3))) S tuples: A__2ND(cons(x0, s(z0))) -> c1(MARK(x0)) A__2ND(cons(x0, cons1(z0, z1))) -> c1(MARK(x0)) A__2ND(cons(x0, s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(x0, cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(cons(z0, z1))) -> c6(A__2ND(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(2nd(s(z0))) -> c6(MARK(s(z0))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, 2nd(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), 2nd(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), 2nd(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, 2nd(x1))) -> c1(MARK(x0)) A__2ND(cons(x0, from(x1))) -> c1(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(x0)) A__2ND(cons(x0, from(2nd(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(from(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(x0)) A__2ND(cons(x0, from(s(z0)))) -> c1(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(x0)) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c1(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(x0)) A__2ND(cons(2nd(z0), from(x1))) -> c1(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(2nd(z0))) A__2ND(cons(from(z0), from(x1))) -> c1(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(z0))) A__2ND(cons(cons(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(cons(z0, z1))) A__2ND(cons(s(z0), from(x1))) -> c1(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(s(z0))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c1(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(cons1(z0, z1))) A__2ND(cons(x0, from(x1))) -> c1(MARK(x0)) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(2nd(x0))) A__2ND(cons(2nd(x0), x1)) -> c1(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(2nd(x0))) A__2ND(cons(2nd(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(2nd(2nd(z0)))) A__2ND(cons(2nd(from(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(2nd(from(z0)))) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(2nd(s(z0)), x1)) -> c1(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(2nd(s(z0)))) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(x0), s(z0))) -> c1(MARK(2nd(x0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c1(MARK(2nd(x0))) A__2ND(cons(from(x0), cons(z0, z1))) -> c1(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(from(x0))) A__2ND(cons(from(x0), x1)) -> c1(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(from(x0))) A__2ND(cons(from(2nd(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(from(2nd(z0)))) A__2ND(cons(from(from(z0)), x1)) -> c1(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(from(from(z0)))) A__2ND(cons(from(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(from(cons(z0, z1)))) A__2ND(cons(from(s(z0)), x1)) -> c1(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(from(s(z0)))) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(from(cons1(z0, z1)))) A__2ND(cons(from(x0), x1)) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), s(z0))) -> c1(MARK(from(x0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c1(MARK(from(x0))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(x0, x1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(cons(2nd(z0), x1))) A__2ND(cons(cons(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(cons(from(z0), x1))) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(cons(cons(z0, z1), x1))) A__2ND(cons(cons(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(cons(s(z0), x1))) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(cons(cons1(z0, z1), x1))) A__2ND(cons(cons(x0, x1), x2)) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), s(z0))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c1(MARK(cons(x0, x1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c1(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(s(x0))) A__2ND(cons(s(2nd(z0)), x1)) -> c1(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(s(2nd(z0)))) A__2ND(cons(s(from(z0)), x1)) -> c1(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(s(from(z0)))) A__2ND(cons(s(cons(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(s(cons(z0, z1)))) A__2ND(cons(s(s(z0)), x1)) -> c1(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(s(s(z0)))) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c1(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(s(cons1(z0, z1)))) A__2ND(cons(s(x0), x1)) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), s(z0))) -> c1(MARK(s(x0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c1(MARK(s(x0))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c1(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(cons1(x0, 2nd(z0)))) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(cons1(x0, from(z0)))) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(cons1(x0, cons(z0, z1)))) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(cons1(x0, s(z0)))) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c1(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(2nd(z0), x1))) A__2ND(cons(cons1(from(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(from(z0), x1))) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(cons1(cons(z0, z1), x1))) A__2ND(cons(cons1(s(z0), x1), x2)) -> c1(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(cons1(s(z0), x1))) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c1(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(cons1(cons1(z0, z1), x1))) A__2ND(cons(cons1(x0, x1), x2)) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), s(z0))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c1(MARK(cons1(x0, x1))) A__2ND(cons(x0, 2nd(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__2nd(mark(z0))))), MARK(2nd(2nd(z0)))) A__2ND(cons(x0, 2nd(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(a__from(mark(z0))))), MARK(2nd(from(z0)))) A__2ND(cons(x0, 2nd(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons(mark(z0), z1)))), MARK(2nd(cons(z0, z1)))) A__2ND(cons(x0, 2nd(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(s(mark(z0))))), MARK(2nd(s(z0)))) A__2ND(cons(x0, 2nd(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__2nd(cons1(mark(z0), mark(z1))))), MARK(2nd(cons1(z0, z1)))) A__2ND(cons(2nd(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(from(z0), 2nd(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(s(z0), 2nd(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(cons1(z0, z1), 2nd(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__2nd(mark(x1)))), MARK(2nd(x1))) A__2ND(cons(x0, 2nd(x1))) -> c2(MARK(2nd(x1))) A__2ND(cons(x0, from(x1))) -> c2(A__2ND(cons1(mark(x0), cons(mark(mark(x1)), from(s(mark(x1)))))), MARK(from(x1))) A__2ND(cons(x0, from(2nd(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__2nd(mark(z0))))), MARK(from(2nd(z0)))) A__2ND(cons(x0, from(from(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(a__from(mark(z0))))), MARK(from(from(z0)))) A__2ND(cons(x0, from(cons(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons(mark(z0), z1)))), MARK(from(cons(z0, z1)))) A__2ND(cons(x0, from(s(z0)))) -> c2(A__2ND(cons1(mark(x0), a__from(s(mark(z0))))), MARK(from(s(z0)))) A__2ND(cons(x0, from(cons1(z0, z1)))) -> c2(A__2ND(cons1(mark(x0), a__from(cons1(mark(z0), mark(z1))))), MARK(from(cons1(z0, z1)))) A__2ND(cons(2nd(z0), from(x1))) -> c2(A__2ND(cons1(a__2nd(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(from(z0), from(x1))) -> c2(A__2ND(cons1(a__from(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons(mark(z0), z1), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(s(z0), from(x1))) -> c2(A__2ND(cons1(s(mark(z0)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(cons1(z0, z1), from(x1))) -> c2(A__2ND(cons1(cons1(mark(z0), mark(z1)), a__from(mark(x1)))), MARK(from(x1))) A__2ND(cons(x0, from(x1))) -> c2(MARK(from(x1))) A__2ND(cons(2nd(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__2nd(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(2nd(x0), x1)) -> c2(A__2ND(cons1(2nd(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(from(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(2nd(s(z0)), x1)) -> c2(A__2ND(cons1(a__2nd(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__2nd(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(2nd(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(2nd(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(from(x0), cons(z0, z1))) -> c2(A__2ND(cons1(a__from(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), x1)) -> c2(A__2ND(cons1(from(mark(x0)), mark(x1))), MARK(x1)) A__2ND(cons(from(2nd(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(from(z0)), x1)) -> c2(A__2ND(cons1(a__from(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(from(s(z0)), x1)) -> c2(A__2ND(cons1(a__from(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(from(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(a__from(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(from(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(from(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons(mark(x0), x1), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__2nd(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons(a__from(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons(mark(z0), z1), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons(s(mark(z0)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons(cons1(mark(z0), mark(z1)), x1), mark(x2))), MARK(x2)) A__2ND(cons(cons(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(s(x0), cons(z0, z1))) -> c2(A__2ND(cons1(s(mark(x0)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(s(2nd(z0)), x1)) -> c2(A__2ND(cons1(s(a__2nd(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(from(z0)), x1)) -> c2(A__2ND(cons1(s(a__from(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons(mark(z0), z1)), mark(x1))), MARK(x1)) A__2ND(cons(s(s(z0)), x1)) -> c2(A__2ND(cons1(s(s(mark(z0))), mark(x1))), MARK(x1)) A__2ND(cons(s(cons1(z0, z1)), x1)) -> c2(A__2ND(cons1(s(cons1(mark(z0), mark(z1))), mark(x1))), MARK(x1)) A__2ND(cons(s(x0), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(s(x0), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) A__2ND(cons(cons1(x0, x1), cons(z0, z1))) -> c2(A__2ND(cons1(cons1(mark(x0), mark(x1)), cons(mark(z0), z1))), MARK(cons(z0, z1))) A__2ND(cons(cons1(x0, 2nd(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__2nd(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, from(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), a__from(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons(mark(z0), z1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, s(z0)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), s(mark(z0))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, cons1(z0, z1)), x2)) -> c2(A__2ND(cons1(cons1(mark(x0), cons1(mark(z0), mark(z1))), mark(x2))), MARK(x2)) A__2ND(cons(cons1(2nd(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__2nd(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(from(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(a__from(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons(mark(z0), z1), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(s(z0), x1), x2)) -> c2(A__2ND(cons1(cons1(s(mark(z0)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(cons1(z0, z1), x1), x2)) -> c2(A__2ND(cons1(cons1(cons1(mark(z0), mark(z1)), mark(x1)), mark(x2))), MARK(x2)) A__2ND(cons(cons1(x0, x1), s(z0))) -> c2(MARK(s(z0))) A__2ND(cons(cons1(x0, x1), cons1(z0, z1))) -> c2(MARK(cons1(z0, z1))) MARK(2nd(2nd(2nd(z0)))) -> c6(A__2ND(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(2nd(2nd(from(z0)))) -> c6(A__2ND(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(2nd(2nd(cons(z0, z1)))) -> c6(A__2ND(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(2nd(2nd(s(z0)))) -> c6(A__2ND(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(2nd(2nd(cons1(z0, z1)))) -> c6(A__2ND(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(2nd(2nd(x0))) -> c6(MARK(2nd(x0))) MARK(2nd(from(x0))) -> c6(A__2ND(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(2nd(from(2nd(z0)))) -> c6(A__2ND(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(2nd(from(from(z0)))) -> c6(A__2ND(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(2nd(from(cons(z0, z1)))) -> c6(A__2ND(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(2nd(from(s(z0)))) -> c6(A__2ND(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(2nd(from(cons1(z0, z1)))) -> c6(A__2ND(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(2nd(from(x0))) -> c6(MARK(from(x0))) MARK(2nd(cons1(x0, 2nd(z0)))) -> c6(A__2ND(cons1(mark(x0), a__2nd(mark(z0)))), MARK(cons1(x0, 2nd(z0)))) MARK(2nd(cons1(x0, from(z0)))) -> c6(A__2ND(cons1(mark(x0), a__from(mark(z0)))), MARK(cons1(x0, from(z0)))) MARK(2nd(cons1(x0, cons(z0, z1)))) -> c6(A__2ND(cons1(mark(x0), cons(mark(z0), z1))), MARK(cons1(x0, cons(z0, z1)))) MARK(2nd(cons1(2nd(z0), x1))) -> c6(A__2ND(cons1(a__2nd(mark(z0)), mark(x1))), MARK(cons1(2nd(z0), x1))) MARK(2nd(cons1(from(z0), x1))) -> c6(A__2ND(cons1(a__from(mark(z0)), mark(x1))), MARK(cons1(from(z0), x1))) MARK(2nd(cons1(cons(z0, z1), x1))) -> c6(A__2ND(cons1(cons(mark(z0), z1), mark(x1))), MARK(cons1(cons(z0, z1), x1))) MARK(2nd(cons1(s(z0), x1))) -> c6(A__2ND(cons1(s(mark(z0)), mark(x1))), MARK(cons1(s(z0), x1))) MARK(2nd(cons1(cons1(z0, z1), x1))) -> c6(A__2ND(cons1(cons1(mark(z0), mark(z1)), mark(x1))), MARK(cons1(cons1(z0, z1), x1))) MARK(2nd(cons1(x0, x1))) -> c6(MARK(cons1(x0, x1))) MARK(2nd(cons1(x0, s(z0)))) -> c6(MARK(cons1(x0, s(z0)))) MARK(2nd(cons1(x0, cons1(z0, z1)))) -> c6(MARK(cons1(x0, cons1(z0, z1)))) A__2ND(cons1(z0, cons(from(y0), z2))) -> c(MARK(from(y0))) A__2ND(cons1(z0, cons(cons(y0, y1), z2))) -> c(MARK(cons(y0, y1))) A__2ND(cons1(z0, cons(s(y0), z2))) -> c(MARK(s(y0))) A__2ND(cons1(z0, cons(cons1(y0, y1), z2))) -> c(MARK(cons1(y0, y1))) A__2ND(cons1(z0, cons(2nd(cons(y0, y1)), z2))) -> c(MARK(2nd(cons(y0, y1)))) A__2ND(cons1(z0, cons(2nd(s(y0)), z2))) -> c(MARK(2nd(s(y0)))) A__2ND(cons1(z0, cons(2nd(2nd(2nd(y0))), z2))) -> c(MARK(2nd(2nd(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(from(y0))), z2))) -> c(MARK(2nd(2nd(from(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(s(y0))), z2))) -> c(MARK(2nd(2nd(s(y0))))) A__2ND(cons1(z0, cons(2nd(2nd(cons1(y0, y1))), z2))) -> c(MARK(2nd(2nd(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(2nd(y0)), z2))) -> c(MARK(2nd(2nd(y0)))) A__2ND(cons1(z0, cons(2nd(from(y0)), z2))) -> c(MARK(2nd(from(y0)))) A__2ND(cons1(z0, cons(2nd(from(2nd(y0))), z2))) -> c(MARK(2nd(from(2nd(y0))))) A__2ND(cons1(z0, cons(2nd(from(from(y0))), z2))) -> c(MARK(2nd(from(from(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons(y0, y1))), z2))) -> c(MARK(2nd(from(cons(y0, y1))))) A__2ND(cons1(z0, cons(2nd(from(s(y0))), z2))) -> c(MARK(2nd(from(s(y0))))) A__2ND(cons1(z0, cons(2nd(from(cons1(y0, y1))), z2))) -> c(MARK(2nd(from(cons1(y0, y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, 2nd(y1))), z2))) -> c(MARK(2nd(cons1(y0, 2nd(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, from(y1))), z2))) -> c(MARK(2nd(cons1(y0, from(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons(y1, y2))))) A__2ND(cons1(z0, cons(2nd(cons1(2nd(y0), y1)), z2))) -> c(MARK(2nd(cons1(2nd(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(from(y0), y1)), z2))) -> c(MARK(2nd(cons1(from(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(s(y0), y1)), z2))) -> c(MARK(2nd(cons1(s(y0), y1)))) A__2ND(cons1(z0, cons(2nd(cons1(cons1(y0, y1), y2)), z2))) -> c(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, y1)), z2))) -> c(MARK(2nd(cons1(y0, y1)))) A__2ND(cons1(z0, cons(2nd(cons1(y0, s(y1))), z2))) -> c(MARK(2nd(cons1(y0, s(y1))))) A__2ND(cons1(z0, cons(2nd(cons1(y0, cons1(y1, y2))), z2))) -> c(MARK(2nd(cons1(y0, cons1(y1, y2))))) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(from(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(x0)) A__2ND(cons(x0, cons(s(z0), x2))) -> c1(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(x0)) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c1(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(x0)) A__2ND(cons(x0, cons(2nd(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__2nd(mark(z0)), x2))), MARK(cons(2nd(z0), x2))) A__2ND(cons(x0, cons(from(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(a__from(mark(z0)), x2))), MARK(cons(from(z0), x2))) A__2ND(cons(x0, cons(cons(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons(mark(z0), z1), x2))), MARK(cons(cons(z0, z1), x2))) A__2ND(cons(x0, cons(s(z0), x2))) -> c2(A__2ND(cons1(mark(x0), cons(s(mark(z0)), x2))), MARK(cons(s(z0), x2))) A__2ND(cons(x0, cons(cons1(z0, z1), x2))) -> c2(A__2ND(cons1(mark(x0), cons(cons1(mark(z0), mark(z1)), x2))), MARK(cons(cons1(z0, z1), x2))) A__2ND(cons(x0, cons(x1, x2))) -> c2(MARK(cons(x1, x2))) A__FROM(from(y0)) -> c4(MARK(from(y0))) A__FROM(cons(y0, y1)) -> c4(MARK(cons(y0, y1))) A__FROM(s(y0)) -> c4(MARK(s(y0))) A__FROM(cons1(y0, y1)) -> c4(MARK(cons1(y0, y1))) A__FROM(2nd(cons(y0, y1))) -> c4(MARK(2nd(cons(y0, y1)))) A__FROM(2nd(s(y0))) -> c4(MARK(2nd(s(y0)))) A__FROM(2nd(2nd(2nd(y0)))) -> c4(MARK(2nd(2nd(2nd(y0))))) A__FROM(2nd(2nd(from(y0)))) -> c4(MARK(2nd(2nd(from(y0))))) A__FROM(2nd(2nd(cons(y0, y1)))) -> c4(MARK(2nd(2nd(cons(y0, y1))))) A__FROM(2nd(2nd(s(y0)))) -> c4(MARK(2nd(2nd(s(y0))))) A__FROM(2nd(2nd(cons1(y0, y1)))) -> c4(MARK(2nd(2nd(cons1(y0, y1))))) A__FROM(2nd(2nd(y0))) -> c4(MARK(2nd(2nd(y0)))) A__FROM(2nd(from(y0))) -> c4(MARK(2nd(from(y0)))) A__FROM(2nd(from(2nd(y0)))) -> c4(MARK(2nd(from(2nd(y0))))) A__FROM(2nd(from(from(y0)))) -> c4(MARK(2nd(from(from(y0))))) A__FROM(2nd(from(cons(y0, y1)))) -> c4(MARK(2nd(from(cons(y0, y1))))) A__FROM(2nd(from(s(y0)))) -> c4(MARK(2nd(from(s(y0))))) A__FROM(2nd(from(cons1(y0, y1)))) -> c4(MARK(2nd(from(cons1(y0, y1))))) A__FROM(2nd(cons1(y0, 2nd(y1)))) -> c4(MARK(2nd(cons1(y0, 2nd(y1))))) A__FROM(2nd(cons1(y0, from(y1)))) -> c4(MARK(2nd(cons1(y0, from(y1))))) A__FROM(2nd(cons1(y0, cons(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons(y1, y2))))) A__FROM(2nd(cons1(2nd(y0), y1))) -> c4(MARK(2nd(cons1(2nd(y0), y1)))) A__FROM(2nd(cons1(from(y0), y1))) -> c4(MARK(2nd(cons1(from(y0), y1)))) A__FROM(2nd(cons1(cons(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons(y0, y1), y2)))) A__FROM(2nd(cons1(s(y0), y1))) -> c4(MARK(2nd(cons1(s(y0), y1)))) A__FROM(2nd(cons1(cons1(y0, y1), y2))) -> c4(MARK(2nd(cons1(cons1(y0, y1), y2)))) A__FROM(2nd(cons1(y0, y1))) -> c4(MARK(2nd(cons1(y0, y1)))) A__FROM(2nd(cons1(y0, s(y1)))) -> c4(MARK(2nd(cons1(y0, s(y1))))) A__FROM(2nd(cons1(y0, cons1(y1, y2)))) -> c4(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons1(z0, z1))) -> c7(A__FROM(cons1(mark(z0), mark(z1))), MARK(cons1(z0, z1))) MARK(from(2nd(x0))) -> c7(A__FROM(2nd(mark(x0))), MARK(2nd(x0))) MARK(from(2nd(2nd(z0)))) -> c7(A__FROM(a__2nd(a__2nd(mark(z0)))), MARK(2nd(2nd(z0)))) MARK(from(2nd(from(z0)))) -> c7(A__FROM(a__2nd(a__from(mark(z0)))), MARK(2nd(from(z0)))) MARK(from(2nd(cons(z0, z1)))) -> c7(A__FROM(a__2nd(cons(mark(z0), z1))), MARK(2nd(cons(z0, z1)))) MARK(from(2nd(s(z0)))) -> c7(A__FROM(a__2nd(s(mark(z0)))), MARK(2nd(s(z0)))) MARK(from(2nd(cons1(z0, z1)))) -> c7(A__FROM(a__2nd(cons1(mark(z0), mark(z1)))), MARK(2nd(cons1(z0, z1)))) MARK(from(from(x0))) -> c7(A__FROM(cons(mark(mark(x0)), from(s(mark(x0))))), MARK(from(x0))) MARK(from(from(x0))) -> c7(A__FROM(from(mark(x0))), MARK(from(x0))) MARK(from(from(2nd(z0)))) -> c7(A__FROM(a__from(a__2nd(mark(z0)))), MARK(from(2nd(z0)))) MARK(from(from(from(z0)))) -> c7(A__FROM(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(from(from(cons(z0, z1)))) -> c7(A__FROM(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(from(from(s(z0)))) -> c7(A__FROM(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(from(from(cons1(z0, z1)))) -> c7(A__FROM(a__from(cons1(mark(z0), mark(z1)))), MARK(from(cons1(z0, z1)))) MARK(cons(cons(y0, y1), z1)) -> c8(MARK(cons(y0, y1))) MARK(cons(s(y0), z1)) -> c8(MARK(s(y0))) MARK(cons(cons1(y0, y1), z1)) -> c8(MARK(cons1(y0, y1))) MARK(cons(2nd(cons(y0, y1)), z1)) -> c8(MARK(2nd(cons(y0, y1)))) MARK(cons(2nd(s(y0)), z1)) -> c8(MARK(2nd(s(y0)))) MARK(cons(2nd(2nd(2nd(y0))), z1)) -> c8(MARK(2nd(2nd(2nd(y0))))) MARK(cons(2nd(2nd(from(y0))), z1)) -> c8(MARK(2nd(2nd(from(y0))))) MARK(cons(2nd(2nd(cons(y0, y1))), z1)) -> c8(MARK(2nd(2nd(cons(y0, y1))))) MARK(cons(2nd(2nd(s(y0))), z1)) -> c8(MARK(2nd(2nd(s(y0))))) MARK(cons(2nd(2nd(cons1(y0, y1))), z1)) -> c8(MARK(2nd(2nd(cons1(y0, y1))))) MARK(cons(2nd(2nd(y0)), z1)) -> c8(MARK(2nd(2nd(y0)))) MARK(cons(2nd(from(y0)), z1)) -> c8(MARK(2nd(from(y0)))) MARK(cons(2nd(from(2nd(y0))), z1)) -> c8(MARK(2nd(from(2nd(y0))))) MARK(cons(2nd(from(from(y0))), z1)) -> c8(MARK(2nd(from(from(y0))))) MARK(cons(2nd(from(cons(y0, y1))), z1)) -> c8(MARK(2nd(from(cons(y0, y1))))) MARK(cons(2nd(from(s(y0))), z1)) -> c8(MARK(2nd(from(s(y0))))) MARK(cons(2nd(from(cons1(y0, y1))), z1)) -> c8(MARK(2nd(from(cons1(y0, y1))))) MARK(cons(2nd(cons1(y0, 2nd(y1))), z1)) -> c8(MARK(2nd(cons1(y0, 2nd(y1))))) MARK(cons(2nd(cons1(y0, from(y1))), z1)) -> c8(MARK(2nd(cons1(y0, from(y1))))) MARK(cons(2nd(cons1(y0, cons(y1, y2))), z1)) -> c8(MARK(2nd(cons1(y0, cons(y1, y2))))) MARK(cons(2nd(cons1(2nd(y0), y1)), z1)) -> c8(MARK(2nd(cons1(2nd(y0), y1)))) MARK(cons(2nd(cons1(from(y0), y1)), z1)) -> c8(MARK(2nd(cons1(from(y0), y1)))) MARK(cons(2nd(cons1(cons(y0, y1), y2)), z1)) -> c8(MARK(2nd(cons1(cons(y0, y1), y2)))) MARK(cons(2nd(cons1(s(y0), y1)), z1)) -> c8(MARK(2nd(cons1(s(y0), y1)))) MARK(cons(2nd(cons1(cons1(y0, y1), y2)), z1)) -> c8(MARK(2nd(cons1(cons1(y0, y1), y2)))) MARK(cons(2nd(cons1(y0, y1)), z1)) -> c8(MARK(2nd(cons1(y0, y1)))) MARK(cons(2nd(cons1(y0, s(y1))), z1)) -> c8(MARK(2nd(cons1(y0, s(y1))))) MARK(cons(2nd(cons1(y0, cons1(y1, y2))), z1)) -> c8(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(cons(from(cons(y0, y1)), z1)) -> c8(MARK(from(cons(y0, y1)))) MARK(cons(from(s(y0)), z1)) -> c8(MARK(from(s(y0)))) MARK(cons(from(cons1(y0, y1)), z1)) -> c8(MARK(from(cons1(y0, y1)))) MARK(cons(from(2nd(y0)), z1)) -> c8(MARK(from(2nd(y0)))) MARK(cons(from(2nd(2nd(y0))), z1)) -> c8(MARK(from(2nd(2nd(y0))))) MARK(cons(from(2nd(from(y0))), z1)) -> c8(MARK(from(2nd(from(y0))))) MARK(cons(from(2nd(cons(y0, y1))), z1)) -> c8(MARK(from(2nd(cons(y0, y1))))) MARK(cons(from(2nd(s(y0))), z1)) -> c8(MARK(from(2nd(s(y0))))) MARK(cons(from(2nd(cons1(y0, y1))), z1)) -> c8(MARK(from(2nd(cons1(y0, y1))))) MARK(cons(from(from(y0)), z1)) -> c8(MARK(from(from(y0)))) MARK(cons(from(from(2nd(y0))), z1)) -> c8(MARK(from(from(2nd(y0))))) 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MARK(cons1(2nd(cons1(cons(y0, y1), y2)), z1)) -> c10(MARK(2nd(cons1(cons(y0, y1), y2)))) MARK(cons1(2nd(cons1(s(y0), y1)), z1)) -> c10(MARK(2nd(cons1(s(y0), y1)))) MARK(cons1(2nd(cons1(cons1(y0, y1), y2)), z1)) -> c10(MARK(2nd(cons1(cons1(y0, y1), y2)))) MARK(cons1(2nd(cons1(y0, y1)), z1)) -> c10(MARK(2nd(cons1(y0, y1)))) MARK(cons1(2nd(cons1(y0, s(y1))), z1)) -> c10(MARK(2nd(cons1(y0, s(y1))))) MARK(cons1(2nd(cons1(y0, cons1(y1, y2))), z1)) -> c10(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(cons1(from(cons(y0, y1)), z1)) -> c10(MARK(from(cons(y0, y1)))) MARK(cons1(from(s(y0)), z1)) -> c10(MARK(from(s(y0)))) MARK(cons1(from(cons1(y0, y1)), z1)) -> c10(MARK(from(cons1(y0, y1)))) MARK(cons1(from(2nd(y0)), z1)) -> c10(MARK(from(2nd(y0)))) MARK(cons1(from(2nd(2nd(y0))), z1)) -> c10(MARK(from(2nd(2nd(y0))))) MARK(cons1(from(2nd(from(y0))), z1)) -> c10(MARK(from(2nd(from(y0))))) MARK(cons1(from(2nd(cons(y0, y1))), z1)) -> c10(MARK(from(2nd(cons(y0, y1))))) MARK(cons1(from(2nd(s(y0))), z1)) -> 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c10(MARK(cons(2nd(from(cons1(y0, y1))), y2))) MARK(cons1(cons(2nd(cons1(y0, 2nd(y1))), y2), z1)) -> c10(MARK(cons(2nd(cons1(y0, 2nd(y1))), y2))) MARK(cons1(cons(2nd(cons1(y0, from(y1))), y2), z1)) -> c10(MARK(cons(2nd(cons1(y0, from(y1))), y2))) MARK(cons1(cons(2nd(cons1(y0, cons(y1, y2))), y3), z1)) -> c10(MARK(cons(2nd(cons1(y0, cons(y1, y2))), y3))) MARK(cons1(cons(2nd(cons1(2nd(y0), y1)), y2), z1)) -> c10(MARK(cons(2nd(cons1(2nd(y0), y1)), y2))) MARK(cons1(cons(2nd(cons1(from(y0), y1)), y2), z1)) -> c10(MARK(cons(2nd(cons1(from(y0), y1)), y2))) MARK(cons1(cons(2nd(cons1(cons(y0, y1), y2)), y3), z1)) -> c10(MARK(cons(2nd(cons1(cons(y0, y1), y2)), y3))) MARK(cons1(cons(2nd(cons1(s(y0), y1)), y2), z1)) -> c10(MARK(cons(2nd(cons1(s(y0), y1)), y2))) MARK(cons1(cons(2nd(cons1(cons1(y0, y1), y2)), y3), z1)) -> c10(MARK(cons(2nd(cons1(cons1(y0, y1), y2)), y3))) MARK(cons1(cons(2nd(cons1(y0, y1)), y2), z1)) -> c10(MARK(cons(2nd(cons1(y0, y1)), y2))) MARK(cons1(cons(2nd(cons1(y0, s(y1))), y2), z1)) -> c10(MARK(cons(2nd(cons1(y0, s(y1))), y2))) MARK(cons1(cons(2nd(cons1(y0, cons1(y1, y2))), y3), z1)) -> c10(MARK(cons(2nd(cons1(y0, cons1(y1, y2))), y3))) MARK(cons1(cons(from(cons(y0, y1)), y2), z1)) -> c10(MARK(cons(from(cons(y0, y1)), y2))) MARK(cons1(cons(from(s(y0)), y1), z1)) -> c10(MARK(cons(from(s(y0)), y1))) MARK(cons1(cons(from(cons1(y0, y1)), y2), z1)) -> c10(MARK(cons(from(cons1(y0, y1)), y2))) MARK(cons1(cons(from(2nd(y0)), y1), z1)) -> c10(MARK(cons(from(2nd(y0)), y1))) MARK(cons1(cons(from(2nd(2nd(y0))), y1), z1)) -> c10(MARK(cons(from(2nd(2nd(y0))), y1))) MARK(cons1(cons(from(2nd(from(y0))), y1), z1)) -> c10(MARK(cons(from(2nd(from(y0))), y1))) MARK(cons1(cons(from(2nd(cons(y0, y1))), y2), z1)) -> c10(MARK(cons(from(2nd(cons(y0, y1))), y2))) MARK(cons1(cons(from(2nd(s(y0))), y1), z1)) -> c10(MARK(cons(from(2nd(s(y0))), y1))) MARK(cons1(cons(from(2nd(cons1(y0, y1))), y2), z1)) -> c10(MARK(cons(from(2nd(cons1(y0, y1))), y2))) MARK(cons1(cons(from(from(y0)), y1), z1)) -> c10(MARK(cons(from(from(y0)), y1))) MARK(cons1(cons(from(from(2nd(y0))), y1), z1)) -> c10(MARK(cons(from(from(2nd(y0))), y1))) MARK(cons1(cons(from(from(from(y0))), y1), z1)) -> c10(MARK(cons(from(from(from(y0))), y1))) MARK(cons1(cons(from(from(cons(y0, y1))), y2), z1)) -> c10(MARK(cons(from(from(cons(y0, y1))), y2))) MARK(cons1(cons(from(from(s(y0))), y1), z1)) -> c10(MARK(cons(from(from(s(y0))), y1))) MARK(cons1(cons(from(from(cons1(y0, y1))), y2), z1)) -> c10(MARK(cons(from(from(cons1(y0, y1))), y2))) MARK(cons1(s(s(y0)), z1)) -> c10(MARK(s(s(y0)))) MARK(cons1(s(cons1(y0, y1)), z1)) -> c10(MARK(s(cons1(y0, y1)))) MARK(cons1(s(2nd(cons(y0, y1))), z1)) -> c10(MARK(s(2nd(cons(y0, y1))))) MARK(cons1(s(2nd(s(y0))), z1)) -> c10(MARK(s(2nd(s(y0))))) MARK(cons1(s(2nd(2nd(2nd(y0)))), z1)) -> c10(MARK(s(2nd(2nd(2nd(y0)))))) MARK(cons1(s(2nd(2nd(from(y0)))), z1)) -> c10(MARK(s(2nd(2nd(from(y0)))))) MARK(cons1(s(2nd(2nd(cons(y0, y1)))), z1)) -> c10(MARK(s(2nd(2nd(cons(y0, y1)))))) MARK(cons1(s(2nd(2nd(s(y0)))), z1)) -> c10(MARK(s(2nd(2nd(s(y0)))))) MARK(cons1(s(2nd(2nd(cons1(y0, y1)))), z1)) -> c10(MARK(s(2nd(2nd(cons1(y0, y1)))))) MARK(cons1(s(2nd(2nd(y0))), z1)) -> c10(MARK(s(2nd(2nd(y0))))) MARK(cons1(s(2nd(from(y0))), z1)) -> c10(MARK(s(2nd(from(y0))))) MARK(cons1(s(2nd(from(2nd(y0)))), z1)) -> c10(MARK(s(2nd(from(2nd(y0)))))) MARK(cons1(s(2nd(from(from(y0)))), z1)) -> c10(MARK(s(2nd(from(from(y0)))))) MARK(cons1(s(2nd(from(cons(y0, y1)))), z1)) -> c10(MARK(s(2nd(from(cons(y0, y1)))))) MARK(cons1(s(2nd(from(s(y0)))), z1)) -> c10(MARK(s(2nd(from(s(y0)))))) MARK(cons1(s(2nd(from(cons1(y0, y1)))), z1)) -> c10(MARK(s(2nd(from(cons1(y0, y1)))))) MARK(cons1(s(2nd(cons1(y0, 2nd(y1)))), z1)) -> c10(MARK(s(2nd(cons1(y0, 2nd(y1)))))) MARK(cons1(s(2nd(cons1(y0, from(y1)))), z1)) -> c10(MARK(s(2nd(cons1(y0, from(y1)))))) MARK(cons1(s(2nd(cons1(y0, cons(y1, y2)))), z1)) -> c10(MARK(s(2nd(cons1(y0, cons(y1, y2)))))) MARK(cons1(s(2nd(cons1(2nd(y0), y1))), z1)) -> c10(MARK(s(2nd(cons1(2nd(y0), y1))))) MARK(cons1(s(2nd(cons1(from(y0), y1))), z1)) -> c10(MARK(s(2nd(cons1(from(y0), y1))))) MARK(cons1(s(2nd(cons1(cons(y0, y1), y2))), z1)) -> c10(MARK(s(2nd(cons1(cons(y0, y1), y2))))) MARK(cons1(s(2nd(cons1(s(y0), y1))), z1)) -> c10(MARK(s(2nd(cons1(s(y0), y1))))) MARK(cons1(s(2nd(cons1(cons1(y0, y1), y2))), z1)) -> c10(MARK(s(2nd(cons1(cons1(y0, y1), y2))))) MARK(cons1(s(2nd(cons1(y0, y1))), z1)) -> c10(MARK(s(2nd(cons1(y0, y1))))) MARK(cons1(s(2nd(cons1(y0, s(y1)))), z1)) -> c10(MARK(s(2nd(cons1(y0, s(y1)))))) MARK(cons1(s(2nd(cons1(y0, cons1(y1, y2)))), z1)) -> c10(MARK(s(2nd(cons1(y0, cons1(y1, y2)))))) MARK(cons1(s(from(cons(y0, y1))), z1)) -> c10(MARK(s(from(cons(y0, y1))))) MARK(cons1(s(from(s(y0))), z1)) -> c10(MARK(s(from(s(y0))))) MARK(cons1(s(from(cons1(y0, y1))), z1)) -> c10(MARK(s(from(cons1(y0, y1))))) MARK(cons1(s(from(2nd(y0))), z1)) -> c10(MARK(s(from(2nd(y0))))) MARK(cons1(s(from(2nd(2nd(y0)))), z1)) -> c10(MARK(s(from(2nd(2nd(y0)))))) MARK(cons1(s(from(2nd(from(y0)))), z1)) -> c10(MARK(s(from(2nd(from(y0)))))) MARK(cons1(s(from(2nd(cons(y0, y1)))), z1)) -> c10(MARK(s(from(2nd(cons(y0, y1)))))) MARK(cons1(s(from(2nd(s(y0)))), z1)) -> c10(MARK(s(from(2nd(s(y0)))))) MARK(cons1(s(from(2nd(cons1(y0, y1)))), z1)) -> c10(MARK(s(from(2nd(cons1(y0, y1)))))) MARK(cons1(s(from(from(y0))), z1)) -> c10(MARK(s(from(from(y0))))) MARK(cons1(s(from(from(2nd(y0)))), z1)) -> c10(MARK(s(from(from(2nd(y0)))))) MARK(cons1(s(from(from(from(y0)))), z1)) -> c10(MARK(s(from(from(from(y0)))))) MARK(cons1(s(from(from(cons(y0, y1)))), z1)) -> c10(MARK(s(from(from(cons(y0, y1)))))) MARK(cons1(s(from(from(s(y0)))), z1)) -> c10(MARK(s(from(from(s(y0)))))) MARK(cons1(s(from(from(cons1(y0, y1)))), z1)) -> c10(MARK(s(from(from(cons1(y0, y1)))))) MARK(cons1(s(cons(cons(y0, y1), y2)), z1)) -> c10(MARK(s(cons(cons(y0, y1), y2)))) MARK(cons1(s(cons(s(y0), y1)), z1)) -> c10(MARK(s(cons(s(y0), y1)))) MARK(cons1(s(cons(cons1(y0, y1), y2)), z1)) -> c10(MARK(s(cons(cons1(y0, y1), y2)))) MARK(cons1(s(cons(2nd(cons(y0, y1)), y2)), z1)) -> c10(MARK(s(cons(2nd(cons(y0, y1)), y2)))) MARK(cons1(s(cons(2nd(s(y0)), y1)), z1)) -> c10(MARK(s(cons(2nd(s(y0)), y1)))) MARK(cons1(s(cons(2nd(2nd(2nd(y0))), y1)), z1)) -> c10(MARK(s(cons(2nd(2nd(2nd(y0))), y1)))) MARK(cons1(s(cons(2nd(2nd(from(y0))), y1)), z1)) -> c10(MARK(s(cons(2nd(2nd(from(y0))), y1)))) MARK(cons1(s(cons(2nd(2nd(cons(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(2nd(cons(y0, y1))), y2)))) MARK(cons1(s(cons(2nd(2nd(s(y0))), y1)), z1)) -> c10(MARK(s(cons(2nd(2nd(s(y0))), y1)))) MARK(cons1(s(cons(2nd(2nd(cons1(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(2nd(cons1(y0, y1))), y2)))) MARK(cons1(s(cons(2nd(2nd(y0)), y1)), z1)) -> c10(MARK(s(cons(2nd(2nd(y0)), y1)))) MARK(cons1(s(cons(2nd(from(y0)), y1)), z1)) -> c10(MARK(s(cons(2nd(from(y0)), y1)))) MARK(cons1(s(cons(2nd(from(2nd(y0))), y1)), z1)) -> c10(MARK(s(cons(2nd(from(2nd(y0))), y1)))) MARK(cons1(s(cons(2nd(from(from(y0))), y1)), z1)) -> c10(MARK(s(cons(2nd(from(from(y0))), y1)))) MARK(cons1(s(cons(2nd(from(cons(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(from(cons(y0, y1))), y2)))) MARK(cons1(s(cons(2nd(from(s(y0))), y1)), z1)) -> c10(MARK(s(cons(2nd(from(s(y0))), y1)))) MARK(cons1(s(cons(2nd(from(cons1(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(from(cons1(y0, y1))), y2)))) MARK(cons1(s(cons(2nd(cons1(y0, 2nd(y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(cons1(y0, 2nd(y1))), y2)))) MARK(cons1(s(cons(2nd(cons1(y0, from(y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(cons1(y0, from(y1))), y2)))) MARK(cons1(s(cons(2nd(cons1(y0, cons(y1, y2))), y3)), z1)) -> c10(MARK(s(cons(2nd(cons1(y0, cons(y1, y2))), y3)))) MARK(cons1(s(cons(2nd(cons1(2nd(y0), y1)), y2)), z1)) -> c10(MARK(s(cons(2nd(cons1(2nd(y0), y1)), y2)))) MARK(cons1(s(cons(2nd(cons1(from(y0), y1)), y2)), z1)) -> c10(MARK(s(cons(2nd(cons1(from(y0), y1)), y2)))) MARK(cons1(s(cons(2nd(cons1(cons(y0, y1), y2)), y3)), z1)) -> c10(MARK(s(cons(2nd(cons1(cons(y0, y1), y2)), y3)))) MARK(cons1(s(cons(2nd(cons1(s(y0), y1)), y2)), z1)) -> c10(MARK(s(cons(2nd(cons1(s(y0), y1)), y2)))) MARK(cons1(s(cons(2nd(cons1(cons1(y0, y1), y2)), y3)), z1)) -> c10(MARK(s(cons(2nd(cons1(cons1(y0, y1), y2)), y3)))) MARK(cons1(s(cons(2nd(cons1(y0, y1)), y2)), z1)) -> c10(MARK(s(cons(2nd(cons1(y0, y1)), y2)))) MARK(cons1(s(cons(2nd(cons1(y0, s(y1))), y2)), z1)) -> c10(MARK(s(cons(2nd(cons1(y0, s(y1))), y2)))) MARK(cons1(s(cons(2nd(cons1(y0, cons1(y1, y2))), y3)), z1)) -> c10(MARK(s(cons(2nd(cons1(y0, cons1(y1, y2))), y3)))) MARK(cons1(s(cons(from(cons(y0, y1)), y2)), z1)) -> c10(MARK(s(cons(from(cons(y0, y1)), y2)))) MARK(cons1(s(cons(from(s(y0)), y1)), z1)) -> c10(MARK(s(cons(from(s(y0)), y1)))) MARK(cons1(s(cons(from(cons1(y0, y1)), y2)), z1)) -> c10(MARK(s(cons(from(cons1(y0, y1)), y2)))) MARK(cons1(s(cons(from(2nd(y0)), y1)), z1)) -> c10(MARK(s(cons(from(2nd(y0)), y1)))) MARK(cons1(s(cons(from(2nd(2nd(y0))), y1)), z1)) -> c10(MARK(s(cons(from(2nd(2nd(y0))), y1)))) MARK(cons1(s(cons(from(2nd(from(y0))), y1)), z1)) -> c10(MARK(s(cons(from(2nd(from(y0))), y1)))) MARK(cons1(s(cons(from(2nd(cons(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(from(2nd(cons(y0, y1))), y2)))) MARK(cons1(s(cons(from(2nd(s(y0))), y1)), z1)) -> c10(MARK(s(cons(from(2nd(s(y0))), y1)))) MARK(cons1(s(cons(from(2nd(cons1(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(from(2nd(cons1(y0, y1))), y2)))) MARK(cons1(s(cons(from(from(y0)), y1)), z1)) -> c10(MARK(s(cons(from(from(y0)), y1)))) MARK(cons1(s(cons(from(from(2nd(y0))), y1)), z1)) -> c10(MARK(s(cons(from(from(2nd(y0))), y1)))) MARK(cons1(s(cons(from(from(from(y0))), y1)), z1)) -> c10(MARK(s(cons(from(from(from(y0))), y1)))) MARK(cons1(s(cons(from(from(cons(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(from(from(cons(y0, y1))), y2)))) MARK(cons1(s(cons(from(from(s(y0))), y1)), z1)) -> c10(MARK(s(cons(from(from(s(y0))), y1)))) MARK(cons1(s(cons(from(from(cons1(y0, y1))), y2)), z1)) -> c10(MARK(s(cons(from(from(cons1(y0, y1))), y2)))) MARK(cons1(z0, cons1(y0, y1))) -> c11(MARK(cons1(y0, y1))) MARK(cons1(z0, 2nd(cons(y0, y1)))) -> c11(MARK(2nd(cons(y0, y1)))) MARK(cons1(z0, 2nd(s(y0)))) -> c11(MARK(2nd(s(y0)))) MARK(cons1(z0, 2nd(2nd(2nd(y0))))) -> c11(MARK(2nd(2nd(2nd(y0))))) MARK(cons1(z0, 2nd(2nd(from(y0))))) -> c11(MARK(2nd(2nd(from(y0))))) MARK(cons1(z0, 2nd(2nd(cons(y0, y1))))) -> c11(MARK(2nd(2nd(cons(y0, y1))))) MARK(cons1(z0, 2nd(2nd(s(y0))))) -> c11(MARK(2nd(2nd(s(y0))))) MARK(cons1(z0, 2nd(2nd(cons1(y0, y1))))) -> c11(MARK(2nd(2nd(cons1(y0, y1))))) MARK(cons1(z0, 2nd(2nd(y0)))) -> c11(MARK(2nd(2nd(y0)))) MARK(cons1(z0, 2nd(from(y0)))) -> c11(MARK(2nd(from(y0)))) MARK(cons1(z0, 2nd(from(2nd(y0))))) -> c11(MARK(2nd(from(2nd(y0))))) MARK(cons1(z0, 2nd(from(from(y0))))) -> c11(MARK(2nd(from(from(y0))))) MARK(cons1(z0, 2nd(from(cons(y0, y1))))) -> c11(MARK(2nd(from(cons(y0, y1))))) MARK(cons1(z0, 2nd(from(s(y0))))) -> c11(MARK(2nd(from(s(y0))))) MARK(cons1(z0, 2nd(from(cons1(y0, y1))))) -> c11(MARK(2nd(from(cons1(y0, y1))))) MARK(cons1(z0, 2nd(cons1(y0, 2nd(y1))))) -> c11(MARK(2nd(cons1(y0, 2nd(y1))))) MARK(cons1(z0, 2nd(cons1(y0, from(y1))))) -> c11(MARK(2nd(cons1(y0, from(y1))))) MARK(cons1(z0, 2nd(cons1(y0, cons(y1, y2))))) -> c11(MARK(2nd(cons1(y0, cons(y1, y2))))) MARK(cons1(z0, 2nd(cons1(2nd(y0), y1)))) -> c11(MARK(2nd(cons1(2nd(y0), y1)))) MARK(cons1(z0, 2nd(cons1(from(y0), y1)))) -> c11(MARK(2nd(cons1(from(y0), y1)))) MARK(cons1(z0, 2nd(cons1(cons(y0, y1), y2)))) -> c11(MARK(2nd(cons1(cons(y0, y1), y2)))) MARK(cons1(z0, 2nd(cons1(s(y0), y1)))) -> c11(MARK(2nd(cons1(s(y0), y1)))) MARK(cons1(z0, 2nd(cons1(cons1(y0, y1), y2)))) -> c11(MARK(2nd(cons1(cons1(y0, y1), y2)))) MARK(cons1(z0, 2nd(cons1(y0, y1)))) -> c11(MARK(2nd(cons1(y0, y1)))) MARK(cons1(z0, 2nd(cons1(y0, s(y1))))) -> c11(MARK(2nd(cons1(y0, s(y1))))) MARK(cons1(z0, 2nd(cons1(y0, cons1(y1, y2))))) -> c11(MARK(2nd(cons1(y0, cons1(y1, y2))))) MARK(cons1(z0, from(cons(y0, y1)))) -> c11(MARK(from(cons(y0, y1)))) MARK(cons1(z0, from(s(y0)))) -> c11(MARK(from(s(y0)))) MARK(cons1(z0, from(cons1(y0, y1)))) -> c11(MARK(from(cons1(y0, y1)))) MARK(cons1(z0, from(2nd(y0)))) -> c11(MARK(from(2nd(y0)))) MARK(cons1(z0, from(2nd(2nd(y0))))) -> c11(MARK(from(2nd(2nd(y0))))) MARK(cons1(z0, from(2nd(from(y0))))) -> c11(MARK(from(2nd(from(y0))))) MARK(cons1(z0, from(2nd(cons(y0, y1))))) -> c11(MARK(from(2nd(cons(y0, y1))))) MARK(cons1(z0, from(2nd(s(y0))))) -> c11(MARK(from(2nd(s(y0))))) MARK(cons1(z0, from(2nd(cons1(y0, y1))))) -> c11(MARK(from(2nd(cons1(y0, y1))))) MARK(cons1(z0, from(from(y0)))) -> c11(MARK(from(from(y0)))) MARK(cons1(z0, from(from(2nd(y0))))) -> c11(MARK(from(from(2nd(y0))))) MARK(cons1(z0, from(from(from(y0))))) -> c11(MARK(from(from(from(y0))))) MARK(cons1(z0, from(from(cons(y0, y1))))) -> c11(MARK(from(from(cons(y0, y1))))) MARK(cons1(z0, from(from(s(y0))))) -> c11(MARK(from(from(s(y0))))) MARK(cons1(z0, from(from(cons1(y0, y1))))) -> c11(MARK(from(from(cons1(y0, y1))))) MARK(cons1(z0, cons(cons(y0, y1), y2))) -> c11(MARK(cons(cons(y0, y1), y2))) MARK(cons1(z0, cons(s(y0), y1))) -> c11(MARK(cons(s(y0), y1))) MARK(cons1(z0, cons(cons1(y0, y1), y2))) -> c11(MARK(cons(cons1(y0, y1), y2))) MARK(cons1(z0, cons(2nd(cons(y0, y1)), y2))) -> c11(MARK(cons(2nd(cons(y0, y1)), y2))) MARK(cons1(z0, cons(2nd(s(y0)), y1))) -> c11(MARK(cons(2nd(s(y0)), y1))) MARK(cons1(z0, cons(2nd(2nd(2nd(y0))), y1))) -> c11(MARK(cons(2nd(2nd(2nd(y0))), y1))) MARK(cons1(z0, cons(2nd(2nd(from(y0))), y1))) -> c11(MARK(cons(2nd(2nd(from(y0))), y1))) MARK(cons1(z0, cons(2nd(2nd(cons(y0, y1))), y2))) -> c11(MARK(cons(2nd(2nd(cons(y0, y1))), y2))) MARK(cons1(z0, cons(2nd(2nd(s(y0))), y1))) -> c11(MARK(cons(2nd(2nd(s(y0))), y1))) MARK(cons1(z0, cons(2nd(2nd(cons1(y0, y1))), y2))) -> c11(MARK(cons(2nd(2nd(cons1(y0, y1))), y2))) MARK(cons1(z0, cons(2nd(2nd(y0)), y1))) -> c11(MARK(cons(2nd(2nd(y0)), y1))) MARK(cons1(z0, cons(2nd(from(y0)), y1))) -> c11(MARK(cons(2nd(from(y0)), y1))) MARK(cons1(z0, cons(2nd(from(2nd(y0))), y1))) -> c11(MARK(cons(2nd(from(2nd(y0))), y1))) MARK(cons1(z0, cons(2nd(from(from(y0))), y1))) -> c11(MARK(cons(2nd(from(from(y0))), y1))) MARK(cons1(z0, cons(2nd(from(cons(y0, y1))), y2))) -> c11(MARK(cons(2nd(from(cons(y0, y1))), y2))) MARK(cons1(z0, cons(2nd(from(s(y0))), y1))) -> c11(MARK(cons(2nd(from(s(y0))), y1))) MARK(cons1(z0, cons(2nd(from(cons1(y0, y1))), y2))) -> c11(MARK(cons(2nd(from(cons1(y0, y1))), y2))) MARK(cons1(z0, cons(2nd(cons1(y0, 2nd(y1))), y2))) -> c11(MARK(cons(2nd(cons1(y0, 2nd(y1))), y2))) MARK(cons1(z0, cons(2nd(cons1(y0, from(y1))), y2))) -> c11(MARK(cons(2nd(cons1(y0, from(y1))), y2))) MARK(cons1(z0, cons(2nd(cons1(y0, cons(y1, y2))), y3))) -> c11(MARK(cons(2nd(cons1(y0, cons(y1, y2))), y3))) MARK(cons1(z0, cons(2nd(cons1(2nd(y0), y1)), y2))) -> c11(MARK(cons(2nd(cons1(2nd(y0), y1)), y2))) MARK(cons1(z0, cons(2nd(cons1(from(y0), y1)), y2))) -> c11(MARK(cons(2nd(cons1(from(y0), 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c11(MARK(cons1(2nd(2nd(cons(y0, y1))), y2))) MARK(cons1(z0, cons1(2nd(2nd(s(y0))), y1))) -> c11(MARK(cons1(2nd(2nd(s(y0))), y1))) MARK(cons1(z0, cons1(2nd(2nd(cons1(y0, y1))), y2))) -> c11(MARK(cons1(2nd(2nd(cons1(y0, y1))), y2))) MARK(cons1(z0, cons1(2nd(2nd(y0)), y1))) -> c11(MARK(cons1(2nd(2nd(y0)), y1))) MARK(cons1(z0, cons1(2nd(from(y0)), y1))) -> c11(MARK(cons1(2nd(from(y0)), y1))) MARK(cons1(z0, cons1(2nd(from(2nd(y0))), y1))) -> c11(MARK(cons1(2nd(from(2nd(y0))), y1))) MARK(cons1(z0, cons1(2nd(from(from(y0))), y1))) -> c11(MARK(cons1(2nd(from(from(y0))), y1))) MARK(cons1(z0, cons1(2nd(from(cons(y0, y1))), y2))) -> c11(MARK(cons1(2nd(from(cons(y0, y1))), y2))) MARK(cons1(z0, cons1(2nd(from(s(y0))), y1))) -> c11(MARK(cons1(2nd(from(s(y0))), y1))) MARK(cons1(z0, cons1(2nd(from(cons1(y0, y1))), y2))) -> c11(MARK(cons1(2nd(from(cons1(y0, y1))), y2))) MARK(cons1(z0, cons1(2nd(cons1(y0, 2nd(y1))), y2))) -> c11(MARK(cons1(2nd(cons1(y0, 2nd(y1))), y2))) MARK(cons1(z0, cons1(2nd(cons1(y0, from(y1))), y2))) -> c11(MARK(cons1(2nd(cons1(y0, from(y1))), y2))) MARK(cons1(z0, cons1(2nd(cons1(y0, cons(y1, y2))), y3))) -> c11(MARK(cons1(2nd(cons1(y0, cons(y1, y2))), y3))) MARK(cons1(z0, cons1(2nd(cons1(2nd(y0), y1)), y2))) -> c11(MARK(cons1(2nd(cons1(2nd(y0), y1)), y2))) MARK(cons1(z0, cons1(2nd(cons1(from(y0), y1)), y2))) -> c11(MARK(cons1(2nd(cons1(from(y0), y1)), y2))) MARK(cons1(z0, cons1(2nd(cons1(cons(y0, y1), y2)), y3))) -> c11(MARK(cons1(2nd(cons1(cons(y0, y1), y2)), y3))) MARK(cons1(z0, cons1(2nd(cons1(s(y0), y1)), y2))) -> c11(MARK(cons1(2nd(cons1(s(y0), y1)), y2))) MARK(cons1(z0, cons1(2nd(cons1(cons1(y0, y1), y2)), y3))) -> c11(MARK(cons1(2nd(cons1(cons1(y0, y1), y2)), y3))) MARK(cons1(z0, cons1(2nd(cons1(y0, y1)), y2))) -> c11(MARK(cons1(2nd(cons1(y0, y1)), y2))) MARK(cons1(z0, cons1(2nd(cons1(y0, s(y1))), y2))) -> c11(MARK(cons1(2nd(cons1(y0, s(y1))), y2))) MARK(cons1(z0, cons1(2nd(cons1(y0, cons1(y1, y2))), y3))) -> c11(MARK(cons1(2nd(cons1(y0, cons1(y1, y2))), y3))) MARK(cons1(z0, cons1(from(cons(y0, y1)), y2))) -> c11(MARK(cons1(from(cons(y0, y1)), y2))) MARK(cons1(z0, cons1(from(s(y0)), y1))) -> c11(MARK(cons1(from(s(y0)), y1))) MARK(cons1(z0, cons1(from(cons1(y0, y1)), y2))) -> c11(MARK(cons1(from(cons1(y0, y1)), y2))) MARK(cons1(z0, cons1(from(2nd(y0)), y1))) -> c11(MARK(cons1(from(2nd(y0)), y1))) MARK(cons1(z0, cons1(from(2nd(2nd(y0))), y1))) -> c11(MARK(cons1(from(2nd(2nd(y0))), y1))) MARK(cons1(z0, cons1(from(2nd(from(y0))), y1))) -> c11(MARK(cons1(from(2nd(from(y0))), y1))) MARK(cons1(z0, cons1(from(2nd(cons(y0, y1))), y2))) -> c11(MARK(cons1(from(2nd(cons(y0, y1))), y2))) MARK(cons1(z0, cons1(from(2nd(s(y0))), y1))) -> c11(MARK(cons1(from(2nd(s(y0))), y1))) MARK(cons1(z0, cons1(from(2nd(cons1(y0, y1))), y2))) -> c11(MARK(cons1(from(2nd(cons1(y0, y1))), y2))) MARK(cons1(z0, cons1(from(from(y0)), y1))) -> c11(MARK(cons1(from(from(y0)), y1))) MARK(cons1(z0, cons1(from(from(2nd(y0))), y1))) -> c11(MARK(cons1(from(from(2nd(y0))), y1))) MARK(cons1(z0, cons1(from(from(from(y0))), y1))) -> c11(MARK(cons1(from(from(from(y0))), y1))) MARK(cons1(z0, cons1(from(from(cons(y0, y1))), y2))) -> c11(MARK(cons1(from(from(cons(y0, y1))), y2))) MARK(cons1(z0, cons1(from(from(s(y0))), y1))) -> c11(MARK(cons1(from(from(s(y0))), y1))) MARK(cons1(z0, cons1(from(from(cons1(y0, y1))), y2))) -> c11(MARK(cons1(from(from(cons1(y0, y1))), y2))) MARK(cons1(z0, cons1(cons(cons(y0, y1), y2), y3))) -> c11(MARK(cons1(cons(cons(y0, y1), y2), y3))) MARK(cons1(z0, cons1(cons(s(y0), y1), y2))) -> c11(MARK(cons1(cons(s(y0), y1), y2))) MARK(cons1(z0, cons1(cons(cons1(y0, y1), y2), y3))) -> c11(MARK(cons1(cons(cons1(y0, y1), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(cons(y0, y1)), y2), y3))) -> c11(MARK(cons1(cons(2nd(cons(y0, y1)), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(s(y0)), y1), y2))) -> c11(MARK(cons1(cons(2nd(s(y0)), y1), y2))) MARK(cons1(z0, cons1(cons(2nd(2nd(2nd(y0))), y1), y2))) -> c11(MARK(cons1(cons(2nd(2nd(2nd(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(2nd(2nd(from(y0))), y1), y2))) -> c11(MARK(cons1(cons(2nd(2nd(from(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(2nd(2nd(cons(y0, y1))), y2), y3))) -> c11(MARK(cons1(cons(2nd(2nd(cons(y0, y1))), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(2nd(s(y0))), y1), y2))) -> c11(MARK(cons1(cons(2nd(2nd(s(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(2nd(2nd(cons1(y0, y1))), y2), y3))) -> c11(MARK(cons1(cons(2nd(2nd(cons1(y0, y1))), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(2nd(y0)), y1), y2))) -> c11(MARK(cons1(cons(2nd(2nd(y0)), y1), y2))) MARK(cons1(z0, cons1(cons(2nd(from(y0)), y1), y2))) -> c11(MARK(cons1(cons(2nd(from(y0)), y1), y2))) MARK(cons1(z0, cons1(cons(2nd(from(2nd(y0))), y1), y2))) -> c11(MARK(cons1(cons(2nd(from(2nd(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(2nd(from(from(y0))), y1), y2))) -> c11(MARK(cons1(cons(2nd(from(from(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(2nd(from(cons(y0, y1))), y2), y3))) -> c11(MARK(cons1(cons(2nd(from(cons(y0, y1))), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(from(s(y0))), y1), y2))) -> c11(MARK(cons1(cons(2nd(from(s(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(2nd(from(cons1(y0, y1))), y2), y3))) -> c11(MARK(cons1(cons(2nd(from(cons1(y0, y1))), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(cons1(y0, 2nd(y1))), y2), y3))) -> c11(MARK(cons1(cons(2nd(cons1(y0, 2nd(y1))), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(cons1(y0, from(y1))), y2), y3))) -> c11(MARK(cons1(cons(2nd(cons1(y0, from(y1))), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(cons1(y0, cons(y1, y2))), y3), y4))) -> c11(MARK(cons1(cons(2nd(cons1(y0, cons(y1, y2))), y3), y4))) MARK(cons1(z0, cons1(cons(2nd(cons1(2nd(y0), y1)), y2), y3))) -> c11(MARK(cons1(cons(2nd(cons1(2nd(y0), y1)), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(cons1(from(y0), y1)), y2), y3))) -> c11(MARK(cons1(cons(2nd(cons1(from(y0), y1)), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(cons1(cons(y0, y1), y2)), y3), y4))) -> c11(MARK(cons1(cons(2nd(cons1(cons(y0, y1), y2)), y3), y4))) MARK(cons1(z0, cons1(cons(2nd(cons1(s(y0), y1)), y2), y3))) -> c11(MARK(cons1(cons(2nd(cons1(s(y0), y1)), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(cons1(cons1(y0, y1), y2)), y3), y4))) -> c11(MARK(cons1(cons(2nd(cons1(cons1(y0, y1), y2)), y3), y4))) MARK(cons1(z0, cons1(cons(2nd(cons1(y0, y1)), y2), y3))) -> c11(MARK(cons1(cons(2nd(cons1(y0, y1)), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(cons1(y0, s(y1))), y2), y3))) -> c11(MARK(cons1(cons(2nd(cons1(y0, s(y1))), y2), y3))) MARK(cons1(z0, cons1(cons(2nd(cons1(y0, cons1(y1, y2))), y3), y4))) -> c11(MARK(cons1(cons(2nd(cons1(y0, cons1(y1, y2))), y3), y4))) MARK(cons1(z0, cons1(cons(from(cons(y0, y1)), y2), y3))) -> c11(MARK(cons1(cons(from(cons(y0, y1)), y2), y3))) MARK(cons1(z0, cons1(cons(from(s(y0)), y1), y2))) -> c11(MARK(cons1(cons(from(s(y0)), y1), y2))) MARK(cons1(z0, cons1(cons(from(cons1(y0, y1)), y2), y3))) -> c11(MARK(cons1(cons(from(cons1(y0, y1)), y2), y3))) MARK(cons1(z0, cons1(cons(from(2nd(y0)), y1), y2))) -> c11(MARK(cons1(cons(from(2nd(y0)), y1), y2))) MARK(cons1(z0, cons1(cons(from(2nd(2nd(y0))), y1), y2))) -> c11(MARK(cons1(cons(from(2nd(2nd(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(from(2nd(from(y0))), y1), y2))) -> c11(MARK(cons1(cons(from(2nd(from(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(from(2nd(cons(y0, y1))), y2), y3))) -> c11(MARK(cons1(cons(from(2nd(cons(y0, y1))), y2), y3))) MARK(cons1(z0, cons1(cons(from(2nd(s(y0))), y1), y2))) -> c11(MARK(cons1(cons(from(2nd(s(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(from(2nd(cons1(y0, y1))), y2), y3))) -> c11(MARK(cons1(cons(from(2nd(cons1(y0, y1))), y2), y3))) MARK(cons1(z0, cons1(cons(from(from(y0)), y1), y2))) -> c11(MARK(cons1(cons(from(from(y0)), y1), y2))) MARK(cons1(z0, cons1(cons(from(from(2nd(y0))), y1), y2))) -> c11(MARK(cons1(cons(from(from(2nd(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(from(from(from(y0))), y1), y2))) -> c11(MARK(cons1(cons(from(from(from(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(from(from(cons(y0, y1))), y2), y3))) -> c11(MARK(cons1(cons(from(from(cons(y0, y1))), y2), y3))) MARK(cons1(z0, cons1(cons(from(from(s(y0))), y1), y2))) -> c11(MARK(cons1(cons(from(from(s(y0))), y1), y2))) MARK(cons1(z0, cons1(cons(from(from(cons1(y0, y1))), y2), y3))) -> c11(MARK(cons1(cons(from(from(cons1(y0, y1))), y2), y3))) MARK(cons1(z0, cons1(s(s(y0)), y1))) -> c11(MARK(cons1(s(s(y0)), y1))) MARK(cons1(z0, cons1(s(cons1(y0, y1)), y2))) -> c11(MARK(cons1(s(cons1(y0, y1)), y2))) MARK(cons1(z0, cons1(s(2nd(cons(y0, y1))), y2))) -> c11(MARK(cons1(s(2nd(cons(y0, y1))), y2))) MARK(cons1(z0, cons1(s(2nd(s(y0))), y1))) -> c11(MARK(cons1(s(2nd(s(y0))), y1))) MARK(cons1(z0, cons1(s(2nd(2nd(2nd(y0)))), y1))) -> c11(MARK(cons1(s(2nd(2nd(2nd(y0)))), y1))) MARK(cons1(z0, cons1(s(2nd(2nd(from(y0)))), y1))) -> c11(MARK(cons1(s(2nd(2nd(from(y0)))), y1))) MARK(cons1(z0, cons1(s(2nd(2nd(cons(y0, y1)))), y2))) -> c11(MARK(cons1(s(2nd(2nd(cons(y0, y1)))), y2))) MARK(cons1(z0, cons1(s(2nd(2nd(s(y0)))), y1))) -> c11(MARK(cons1(s(2nd(2nd(s(y0)))), y1))) MARK(cons1(z0, cons1(s(2nd(2nd(cons1(y0, y1)))), y2))) -> c11(MARK(cons1(s(2nd(2nd(cons1(y0, y1)))), y2))) MARK(cons1(z0, cons1(s(2nd(2nd(y0))), y1))) -> c11(MARK(cons1(s(2nd(2nd(y0))), y1))) MARK(cons1(z0, cons1(s(2nd(from(y0))), y1))) -> c11(MARK(cons1(s(2nd(from(y0))), y1))) MARK(cons1(z0, cons1(s(2nd(from(2nd(y0)))), y1))) -> c11(MARK(cons1(s(2nd(from(2nd(y0)))), y1))) MARK(cons1(z0, cons1(s(2nd(from(from(y0)))), y1))) -> c11(MARK(cons1(s(2nd(from(from(y0)))), y1))) MARK(cons1(z0, cons1(s(2nd(from(cons(y0, y1)))), y2))) -> c11(MARK(cons1(s(2nd(from(cons(y0, y1)))), y2))) MARK(cons1(z0, cons1(s(2nd(from(s(y0)))), y1))) -> c11(MARK(cons1(s(2nd(from(s(y0)))), y1))) MARK(cons1(z0, cons1(s(2nd(from(cons1(y0, y1)))), y2))) -> c11(MARK(cons1(s(2nd(from(cons1(y0, y1)))), y2))) MARK(cons1(z0, cons1(s(2nd(cons1(y0, 2nd(y1)))), y2))) -> c11(MARK(cons1(s(2nd(cons1(y0, 2nd(y1)))), y2))) MARK(cons1(z0, cons1(s(2nd(cons1(y0, from(y1)))), y2))) -> c11(MARK(cons1(s(2nd(cons1(y0, from(y1)))), y2))) MARK(cons1(z0, cons1(s(2nd(cons1(y0, cons(y1, y2)))), y3))) -> c11(MARK(cons1(s(2nd(cons1(y0, cons(y1, y2)))), y3))) MARK(cons1(z0, cons1(s(2nd(cons1(2nd(y0), y1))), y2))) -> c11(MARK(cons1(s(2nd(cons1(2nd(y0), y1))), y2))) MARK(cons1(z0, cons1(s(2nd(cons1(from(y0), y1))), y2))) -> c11(MARK(cons1(s(2nd(cons1(from(y0), y1))), y2))) MARK(cons1(z0, cons1(s(2nd(cons1(cons(y0, y1), y2))), y3))) -> c11(MARK(cons1(s(2nd(cons1(cons(y0, y1), y2))), y3))) MARK(cons1(z0, cons1(s(2nd(cons1(s(y0), y1))), y2))) -> c11(MARK(cons1(s(2nd(cons1(s(y0), y1))), y2))) MARK(cons1(z0, cons1(s(2nd(cons1(cons1(y0, y1), y2))), y3))) -> c11(MARK(cons1(s(2nd(cons1(cons1(y0, y1), y2))), y3))) MARK(cons1(z0, cons1(s(2nd(cons1(y0, y1))), y2))) -> c11(MARK(cons1(s(2nd(cons1(y0, y1))), y2))) MARK(cons1(z0, cons1(s(2nd(cons1(y0, s(y1)))), y2))) -> c11(MARK(cons1(s(2nd(cons1(y0, s(y1)))), y2))) MARK(cons1(z0, cons1(s(2nd(cons1(y0, cons1(y1, y2)))), y3))) -> c11(MARK(cons1(s(2nd(cons1(y0, cons1(y1, y2)))), y3))) MARK(cons1(z0, cons1(s(from(cons(y0, y1))), y2))) -> c11(MARK(cons1(s(from(cons(y0, y1))), y2))) MARK(cons1(z0, cons1(s(from(s(y0))), y1))) -> c11(MARK(cons1(s(from(s(y0))), y1))) MARK(cons1(z0, cons1(s(from(cons1(y0, y1))), y2))) -> c11(MARK(cons1(s(from(cons1(y0, y1))), y2))) MARK(cons1(z0, cons1(s(from(2nd(y0))), y1))) -> c11(MARK(cons1(s(from(2nd(y0))), y1))) MARK(cons1(z0, cons1(s(from(2nd(2nd(y0)))), y1))) -> c11(MARK(cons1(s(from(2nd(2nd(y0)))), y1))) MARK(cons1(z0, cons1(s(from(2nd(from(y0)))), y1))) -> c11(MARK(cons1(s(from(2nd(from(y0)))), y1))) MARK(cons1(z0, cons1(s(from(2nd(cons(y0, y1)))), y2))) -> c11(MARK(cons1(s(from(2nd(cons(y0, y1)))), y2))) MARK(cons1(z0, cons1(s(from(2nd(s(y0)))), y1))) -> c11(MARK(cons1(s(from(2nd(s(y0)))), y1))) MARK(cons1(z0, cons1(s(from(2nd(cons1(y0, y1)))), y2))) -> c11(MARK(cons1(s(from(2nd(cons1(y0, y1)))), y2))) MARK(cons1(z0, cons1(s(from(from(y0))), y1))) -> c11(MARK(cons1(s(from(from(y0))), y1))) MARK(cons1(z0, cons1(s(from(from(2nd(y0)))), y1))) -> c11(MARK(cons1(s(from(from(2nd(y0)))), y1))) MARK(cons1(z0, cons1(s(from(from(from(y0)))), y1))) -> c11(MARK(cons1(s(from(from(from(y0)))), y1))) MARK(cons1(z0, cons1(s(from(from(cons(y0, y1)))), y2))) -> c11(MARK(cons1(s(from(from(cons(y0, y1)))), y2))) MARK(cons1(z0, cons1(s(from(from(s(y0)))), y1))) -> c11(MARK(cons1(s(from(from(s(y0)))), y1))) MARK(cons1(z0, cons1(s(from(from(cons1(y0, y1)))), y2))) -> c11(MARK(cons1(s(from(from(cons1(y0, y1)))), y2))) MARK(cons1(z0, cons1(s(cons(cons(y0, y1), y2)), y3))) -> c11(MARK(cons1(s(cons(cons(y0, y1), y2)), y3))) MARK(cons1(z0, cons1(s(cons(s(y0), y1)), y2))) -> c11(MARK(cons1(s(cons(s(y0), y1)), y2))) MARK(cons1(z0, cons1(s(cons(cons1(y0, y1), y2)), y3))) -> c11(MARK(cons1(s(cons(cons1(y0, y1), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(cons(y0, y1)), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(cons(y0, y1)), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(s(y0)), y1)), y2))) -> c11(MARK(cons1(s(cons(2nd(s(y0)), y1)), y2))) MARK(cons1(z0, cons1(s(cons(2nd(2nd(2nd(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(2nd(2nd(2nd(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(2nd(2nd(from(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(2nd(2nd(from(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(2nd(2nd(cons(y0, y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(2nd(cons(y0, y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(2nd(s(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(2nd(2nd(s(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(2nd(2nd(cons1(y0, y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(2nd(cons1(y0, y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(2nd(y0)), y1)), y2))) -> c11(MARK(cons1(s(cons(2nd(2nd(y0)), y1)), y2))) MARK(cons1(z0, cons1(s(cons(2nd(from(y0)), y1)), y2))) -> c11(MARK(cons1(s(cons(2nd(from(y0)), y1)), y2))) MARK(cons1(z0, cons1(s(cons(2nd(from(2nd(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(2nd(from(2nd(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(2nd(from(from(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(2nd(from(from(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(2nd(from(cons(y0, y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(from(cons(y0, y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(from(s(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(2nd(from(s(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(2nd(from(cons1(y0, y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(from(cons1(y0, y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(y0, 2nd(y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(cons1(y0, 2nd(y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(y0, from(y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(cons1(y0, from(y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(y0, cons(y1, y2))), y3)), y4))) -> c11(MARK(cons1(s(cons(2nd(cons1(y0, cons(y1, y2))), y3)), y4))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(2nd(y0), y1)), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(cons1(2nd(y0), y1)), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(from(y0), y1)), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(cons1(from(y0), y1)), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(cons(y0, y1), y2)), y3)), y4))) -> c11(MARK(cons1(s(cons(2nd(cons1(cons(y0, y1), y2)), y3)), y4))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(s(y0), y1)), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(cons1(s(y0), y1)), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(cons1(y0, y1), y2)), y3)), y4))) -> c11(MARK(cons1(s(cons(2nd(cons1(cons1(y0, y1), y2)), y3)), y4))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(y0, y1)), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(cons1(y0, y1)), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(y0, s(y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(2nd(cons1(y0, s(y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(2nd(cons1(y0, cons1(y1, y2))), y3)), y4))) -> c11(MARK(cons1(s(cons(2nd(cons1(y0, cons1(y1, y2))), y3)), y4))) MARK(cons1(z0, cons1(s(cons(from(cons(y0, y1)), y2)), y3))) -> c11(MARK(cons1(s(cons(from(cons(y0, y1)), y2)), y3))) MARK(cons1(z0, cons1(s(cons(from(s(y0)), y1)), y2))) -> c11(MARK(cons1(s(cons(from(s(y0)), y1)), y2))) MARK(cons1(z0, cons1(s(cons(from(cons1(y0, y1)), y2)), y3))) -> c11(MARK(cons1(s(cons(from(cons1(y0, y1)), y2)), y3))) MARK(cons1(z0, cons1(s(cons(from(2nd(y0)), y1)), y2))) -> c11(MARK(cons1(s(cons(from(2nd(y0)), y1)), y2))) MARK(cons1(z0, cons1(s(cons(from(2nd(2nd(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(from(2nd(2nd(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(from(2nd(from(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(from(2nd(from(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(from(2nd(cons(y0, y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(from(2nd(cons(y0, y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(from(2nd(s(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(from(2nd(s(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(from(2nd(cons1(y0, y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(from(2nd(cons1(y0, y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(from(from(y0)), y1)), y2))) -> c11(MARK(cons1(s(cons(from(from(y0)), y1)), y2))) MARK(cons1(z0, cons1(s(cons(from(from(2nd(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(from(from(2nd(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(from(from(from(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(from(from(from(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(from(from(cons(y0, y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(from(from(cons(y0, y1))), y2)), y3))) MARK(cons1(z0, cons1(s(cons(from(from(s(y0))), y1)), y2))) -> c11(MARK(cons1(s(cons(from(from(s(y0))), y1)), y2))) MARK(cons1(z0, cons1(s(cons(from(from(cons1(y0, y1))), y2)), y3))) -> c11(MARK(cons1(s(cons(from(from(cons1(y0, y1))), y2)), y3))) K tuples:none Defined Rule Symbols: a__2nd_1, a__from_1, mark_1 Defined Pair Symbols: A__2ND_1, MARK_1, A__FROM_1 Compound Symbols: c1_1, c2_1, c6_2, c6_1, c1_2, c2_2, c_1, c4_1, c7_2, c8_1, c9_1, c10_1, c11_1